fluid

Fluid friction, also known as viscous friction or fluid resistance, is the force that resists the motion of an object through a fluid due to the internal friction within the fluid. It is an essential concept in fields such as fluid mechanics, aerodynamics, and hydrodynamics, and understanding its principles is crucial for designing efficient systems and predicting the behavior of objects moving through fluids.

Viscosity: The Key to Fluid Friction

Viscosity is a fundamental property of fluids that directly influences fluid friction. It is defined as the measure of a fluid’s resistance to flow, or the ratio of the shear stress to the shear rate of the fluid. The SI unit of viscosity is the pascal-second (Pa·s), while the US customary system uses the pound-second per square foot (lb·s/ft²).

Dynamic Viscosity

Dynamic viscosity, also known as absolute viscosity, is the viscosity of a fluid under normal conditions. It is denoted by the Greek letter eta (η) and has the same units as viscosity, Pa·s or lb·s/ft².

Kinematic Viscosity

Kinematic viscosity is the ratio of dynamic viscosity to fluid density. It is denoted by the Greek letter nu (ν) and has the unit of square meters per second (m²/s) or square feet per second (ft²/s) in the SI and US customary systems, respectively.

Fluid Friction Coefficient: Quantifying Resistance

The fluid friction coefficient, also known as the drag coefficient, is a dimensionless quantity that characterizes the resistance of a fluid to the motion of an object through it. It depends on various factors, such as the shape and size of the object, the fluid properties, and the flow conditions.

Factors Affecting Fluid Friction Coefficient

1. Shape of the object: The shape of the object significantly influences the fluid friction coefficient. Streamlined shapes, such as airfoils and hydrofoils, generally have lower drag coefficients compared to blunt shapes, like spheres and cubes.
2. Size of the object: The size of the object also affects the fluid friction coefficient. Larger objects typically have higher drag coefficients due to the increased surface area exposed to the fluid.
3. Fluid properties: The properties of the fluid, such as viscosity and density, can influence the fluid friction coefficient. Fluids with higher viscosity and density generally result in higher drag coefficients.
4. Flow conditions: The flow regime, whether laminar or turbulent, can also affect the fluid friction coefficient. Turbulent flow typically leads to higher drag coefficients compared to laminar flow.

Reynolds Number: Characterizing Flow Regimes

The Reynolds number is a dimensionless quantity that characterizes the flow regime of a fluid. It is defined as the ratio of inertial forces to viscous forces in the fluid. The critical Reynolds number, which separates laminar flow from turbulent flow, is approximately 2000 for pipe flow and 500,000 for boundary layer flow.

Calculating Reynolds Number

The Reynolds number (Re) is calculated using the formula:

Re = ρ * v * L / μ

Where:
– ρ (rho) is the fluid density (kg/m³)
– v is the fluid velocity (m/s)
– L is the characteristic length of the object (m)
– μ is the dynamic viscosity of the fluid (Pa·s)

Fluid Friction Force: Quantifying the Resistance

The fluid friction force is the force that resists the motion of an object through a fluid due to fluid friction. It is given by the formula:

F = Cd * ρ/2 * A * v^2

Where:
– F is the fluid friction force (N or lb)
– Cd is the drag coefficient (dimensionless)
– ρ is the fluid density (kg/m³ or lb/ft³)
– A is the cross-sectional area of the object (m² or ft²)
– v is the velocity of the object relative to the fluid (m/s or ft/s)

Examples of Fluid Friction Force

1. Viscosity of water: The dynamic viscosity of water at 20°C is approximately 1.002 mPa·s (millipascal-second) or 0.00672 lb·s/ft² in the SI and US customary systems, respectively.
2. Viscosity of oil: The dynamic viscosity of motor oil can range from 10 mPa·s to 1000 mPa·s or more, depending on the type and temperature.
3. Drag coefficient of a sphere: The drag coefficient of a sphere in laminar flow is approximately 0.44, and in turbulent flow it can range from 0.1 to 0.5, depending on the Reynolds number.
4. Fluid friction force on a car: The fluid friction force on a car traveling at 60 mph (26.8 m/s) on a level road is approximately 1300 N (newtons) or 293 lb (pounds), assuming a drag coefficient of 0.3, a frontal area of 2.2 m², and an air density of 1.225 kg/m³.

Numerical Problems and Exercises

To further solidify your understanding of fluid friction, here are some numerical problems and exercises:

1. Calculating Kinematic Viscosity: A fluid has a dynamic viscosity of 0.85 Pa·s and a density of 950 kg/m³. Calculate the kinematic viscosity of the fluid.

2. Determining Drag Coefficient: An object with a cross-sectional area of 0.2 m² is moving through a fluid with a density of 1.2 kg/m³ at a velocity of 15 m/s. The fluid friction force acting on the object is 120 N. Calculate the drag coefficient of the object.

3. Estimating Fluid Friction Force: A spherical object with a diameter of 0.1 m is moving through water at a velocity of 2 m/s. Assuming the dynamic viscosity of water is 1.002 mPa·s and the density is 1000 kg/m³, calculate the fluid friction force acting on the object.

4. Analyzing the Effect of Velocity: Determine how the fluid friction force on a car changes as the velocity increases from 50 mph to 70 mph, assuming a constant drag coefficient of 0.3 and a frontal area of 2.2 m².

By working through these problems and exercises, you will gain a deeper understanding of the various factors that influence fluid friction and how to apply the relevant formulas and principles to real-world scenarios.

Reference:

1. Viscosity and Fluid Friction
2. Fluid Friction and Drag
3. Fluid Mechanics and Hydraulics

Fluid friction, also known as viscous drag, is the frictional force exerted by fluids, while sliding friction is the resistance created between any two objects when they are sliding against each other. This comprehensive guide delves into the intricate details of these two types of friction, providing a thorough understanding for physics students.

Understanding Fluid Friction

Fluid friction, or viscous drag, is the force that arises due to the internal friction between layers of fluid that are moving relative to each other. This friction is caused by the intermolecular forces between the particles within the fluid, which is known as viscosity.

Viscosity and Its Measurement

Viscosity is a measure of a fluid’s resistance to flow. Fluids with high viscosity, such as honey or syrup, have a higher resistance to flow and experience more fluid friction. Conversely, fluids with low viscosity, like water or fruit juice, have a lower resistance to flow and experience less fluid friction.

The viscosity of a fluid can be measured in various units, including poise and pascal-seconds (Pa·s). For example, the viscosity of water at room temperature is approximately 1 centipoise (cP), while the viscosity of honey is around 10,000 cP.

Factors Affecting Fluid Friction

The amount of fluid friction experienced by an object depends on several factors:

1. Fluid Viscosity: As mentioned earlier, the higher the viscosity of the fluid, the greater the fluid friction.
2. Relative Velocity: The faster the object moves through the fluid, the greater the fluid friction.
3. Surface Area: The larger the surface area of the object in contact with the fluid, the greater the fluid friction.
4. Fluid Density: The higher the density of the fluid, the greater the fluid friction.

Calculating Fluid Friction

The fluid friction force (F) experienced by an object moving through a fluid can be calculated using the following formula:

F = 6πηrv

Where:
– η (eta) is the dynamic viscosity of the fluid (in Pa·s or N·s/m²)
– r is the radius of the object (in meters)
– v is the relative velocity between the object and the fluid (in m/s)

This formula is known as Stokes’ law and is applicable for objects moving at low Reynolds numbers (Re < 1), where the flow is laminar.

Reynolds Number and Fluid Flow Regimes

The Reynolds number (Re) is a dimensionless parameter that is used to determine the flow regime of a fluid (laminar or turbulent). It is calculated using the formula:

Re = ρvd/μ

Where:
– ρ (rho) is the density of the fluid (in kg/m³)
– v is the velocity of the object (in m/s)
– d is the diameter of the object (in meters)
– μ (mu) is the dynamic viscosity of the fluid (in Pa·s or N·s/m²)

When the Reynolds number is low (Re < 2300), the flow is considered laminar, and Stokes’ law can be used to calculate the fluid friction. When the Reynolds number is high (Re > 4000), the flow becomes turbulent, and the fluid friction can be calculated using different formulas.

Understanding Sliding Friction

Sliding friction, on the other hand, is the resistance that is created between any two objects when they are sliding against each other. This friction is caused by the interactions between the molecules of the solid surfaces and the molecules of the fluid (such as air or lubricant) between them.

Coefficient of Sliding Friction

The force of sliding friction (F) is defined as the product of the coefficient of sliding friction (μ) and the normal force (N) acting on the surfaces:

F = μ × N

The coefficient of sliding friction is a dimensionless quantity that depends on the materials in contact and the conditions of the contact. It typically ranges from 0 to 1, with higher values indicating greater friction.

Factors Affecting Sliding Friction

The coefficient of sliding friction can be influenced by several factors:

1. Surface Roughness: Rougher surfaces generally have higher coefficients of sliding friction.
2. Lubrication: The presence of a lubricant between the surfaces can significantly reduce the coefficient of sliding friction.
3. Temperature: Increased temperature can affect the coefficient of sliding friction, either increasing or decreasing it, depending on the materials involved.
4. Humidity: The presence of moisture can also influence the coefficient of sliding friction.

Measuring Sliding Friction

The coefficient of sliding friction can be measured experimentally using various methods, such as the inclined plane method or the block-on-plane method. Typical values for the coefficient of sliding friction include:

• Dry steel on dry steel: ~0.5
• Wet glass on wet glass: ~0.04
• Teflon on Teflon: ~0.04

Applications of Sliding Friction

Sliding friction plays a crucial role in various engineering applications, such as:

1. Braking Systems: Sliding friction is the primary mechanism behind the braking of vehicles, where the brake pads apply a normal force to the rotating brake discs or drums, causing them to slow down or stop.
2. Traction and Locomotion: Sliding friction between the tires and the road surface is essential for the traction and movement of vehicles, as well as for the locomotion of various animals and machines.
3. Mechanical Joints and Bearings: Sliding friction is a consideration in the design and operation of mechanical joints and bearings, where it can affect the efficiency and wear of the components.

By understanding the detailed explanations of fluid friction and sliding friction, physics students can gain a comprehensive knowledge of these fundamental concepts and their applications in various fields of study and engineering.

Reference:

1. Fluid Friction | Definition, Types & Example – Lesson – Study.com
2. Viscosity is, essentially, liquid friction – Galileo
3. Fluid Friction And Sliding Friction: Detailed Explanations – YouTube
4. Types Of Friction – Static, Sliding, Rolling And Fluid Friction – BYJU’S
5. A simple measurement of the sliding friction coefficient – ResearchGate

In this article fluid pressure example and their detailed facts are going to be illustrated in an easy manner.

Before fluid pressure example are described elaborately the basic idea of fluid pressure should be clarified. Fluid pressure at a point of a fluid (liquids or gasses) is defined as the normal force(F) exerted per unit area(A) of the fluid containing that point. Fluid pressure P can be defined as, P=F/A …..(1)and it is measured in pascal(N/m^2) in SI.

6+ fluid pressure example with details are written below:

• 1.Hydraulic brakes
• 2.Hydraulic head
• 3.Pressure washing
• 4.Pythagorean cup
• 5. Blood pressure
• 6. Artesian well

Fluids can be divided into two branches. One is fluid statics and another is fluid dynamics. In case of fluid statics the fluids do not have a motion and they are usually static in nature. Pressure of these kinds of static fluids is known as hydrostatic pressure. Those fluids which have a dynamic flow come under the fluid dynamics branch.

scientist Bernoulli has given basic idea of fluid pressure in his Bernoulli’s equation that states that for an ideal(no frictional force is acting on the fluid), incompressible and non viscous liquid the sum of pressure energy(p/ᑭ),kinetic energy(1/2v^2) and potential energy(gh) per unit mass is constant.

                                                      p/ᑭ+1/2v^2+gh= constant …..(2)where ᑭ is the density and v is the velocity of the liquid. g is gravitational acceleration. Dividing equation (2) by g we get-                                      

p/ᑭg+v^2/2g+h=constant……(3) where p/ᑭg is the pressure head and v^2/2g is the velocity head.

1.Hydraulic brakes

A basic hydraulic brake contains pedal,cylinder 1,cylinder 2,pipelines and brake shoes. When a driver applies pressure on the pedal the piston which is inside cylinder 1 pressurizes the fluid to flow inside the cylinder. This cylinder 1 is also known as the master cylinder. After this the brake fluid flows from cylinder 1 to cylinder 2.

The pipelines help in transferring the fluid from cylinder 1 to cylinder 2. There are pistons available inside the cylinders. Due to this transfer of fluid these pistons expand which in turn increase their fluid pressure. As the pistons move,the brake shoes that are kept inside the drum start expanding. This in turn produces frictional force in between the brake shoes and the drum. This makes the wheels stop. These hydraulic brakes are advantageous in a number of ways. That are-

i. They can operate very smoothly

 ii. They have a very simple construction

iii. They can operate at a low effort and

Iv. Their losses due to friction are very less.

This is why hydraulic brakes are one of the important fluid pressure example.

2.Hydraulic head

Hydraulic head is another most important fluid pressure example. It is primarily the pressure of a vertical column of fluid. By measuring the height of the column we will be able to find the pressure of that column. Head refers to the energy associated with the fluid pressure of an incompressible fluid in fluid dynamics.

In bernoulli’s equation the three terms describe different heads. But the head does not signify the value of energy per unit mass. There are four kinds of heads –

A.p/ᑭg is the pressure head. Pressure head is due to static pressure acting on a fluid.

B. v^2/2g refers to the velocity head. It means that dynamic pressure is equivalent to the velocity head of a fluid.

C. The downward force acting on a body due to gravitational acceleration i.e, the weight of the body is known as the elevation head.

D. Friction head refers to the head due to friction between fluid and its medium through which it is flowing.

3.Pressure washing

Pressure washing is actually a water spray that works on high pressure to clean buildings,vehicles,parking areas,roofs etc and remove dust,dirt,oil etc from them. We know that fluid pressure increases with the increase in height. So whenever a dirty place needs to be cleaned, water pressure is applied to it from a longer distance.

Most difficult tasks of cleaning can be done using this technique. It is the third most important fluid pressure example.

4.Pythagorean cup

The mechanism behind the working of a Pythagorean cup is the pascal’s communicating principle. In this a hollow vertical tube is there which has a small opening. When this cup is filled with liquid beyond the vertical tube all the liquids drain out through the small opening in the base. Basically this creates a siphon which helps the liquid to drain out from the base. It is another notable fluid pressure example.

Fluid hydrostatic pressure example

Fluid pressure example of hydrostatic pressure are described below:

 5. Blood pressure

Blood pressure is basically the pressure of blood that is produced by the pumping of the heart which then disseminates in the large arteries of our body. We know that there are two types of blood pressures. One is the systolic or maximum pressure and the other is the diastolic blood pressure.

Hydrostatic pressure of blood is the reason behind the production of the pressure of blood flow against the walls of the arteries in our body.  Hydrostatic pressure is very high near the heart but the narrow path of the arterioles slow down the rate of flow of blood through them. When the blood enters into the arteries during systole the artery walls stretch themselves to handle the extra pressure applied by the flow of extra blood through them. As the walls are elastic in nature they tend to back to their original shape during diastole.

6. Artesian well

Artesian well is another fluid pressure example in which hydrostatic pressure is concerned. Basically these types of wells contain groundwater within them and positive pressure is applied to these. These wells are made up of layers of woods and clays which apply positive pressure to the water of the well.

This pressure helps the water within the well pipes to move in upward direction and to rise above the height of hydrostatic equilibrium point.

Click to read more on 6+ Center Of Pressure Example.

Also Read:

• Low viscosity fluids
• Fluid friction and sliding friction detailed explanations
• Viscosity of newtonian fluid
• Fluid friction and surface area
• Fluid friction of an object
• Viscosity of a fluid
• Fluids density

Fluid friction and surface area are closely interrelated concepts in physics, with the surface area of an object immersed in a fluid directly affecting the amount of friction it experiences. Understanding the relationship between these two factors is crucial for various applications, from aerodynamic design to fluid dynamics analysis.

Understanding Fluid Friction

Fluid friction, also known as viscous drag, is the force that opposes the relative motion between a fluid and a solid surface. This force arises due to the viscosity of the fluid and the no-slip condition at the fluid-solid interface, where the fluid molecules in contact with the surface have zero velocity relative to the surface.

The magnitude of fluid friction depends on several factors, including:

1. Fluid Viscosity: The higher the viscosity of the fluid, the greater the fluid friction experienced by the object.
2. Fluid Velocity: The faster the fluid is moving relative to the object, the greater the fluid friction.
3. Surface Roughness: Rougher surfaces tend to experience higher fluid friction due to increased turbulence and boundary layer separation.
4. Object Shape: The shape of the object can significantly impact the fluid friction, with streamlined shapes generally experiencing lower fluid friction.

Quantifying Fluid Friction: The Reynolds Number

One of the most important parameters used to quantify fluid friction is the Reynolds number (Re or NR), a dimensionless quantity that compares the relative importance of inertial and viscous forces in a fluid flow. The Reynolds number is defined as:

NR = ρ0 v L / η

Where:
– ρ0 is the fluid density (kg/m³)
– v is the fluid velocity (m/s)
– L is a characteristic length of the object perpendicular to the fluid flow (m)
– η is the dynamic viscosity of the fluid (Pa·s or N·s/m²)

The Reynolds number can be used to predict the flow regime and the dominant forces in a fluid flow:

• Low Reynolds Number (NR < 1): Viscous forces dominate, and the flow is typically laminar and smooth.
• High Reynolds Number (NR > 1): Inertial forces dominate, and the flow is often turbulent and chaotic.

Understanding the Reynolds number is crucial for analyzing fluid friction, as it helps determine the appropriate equations and models to use for a given situation.

Fluid Friction and Surface Area

The surface area of an object immersed in a fluid plays a significant role in determining the fluid friction experienced by the object. The relationship between surface area and fluid friction can be expressed through the drag force equation:

Fdrag = 1/2 CD ρ0 A v²

Where:
– Fdrag is the drag force (N)
– CD is the drag coefficient (dimensionless)
– ρ0 is the fluid density (kg/m³)
– A is the cross-sectional area of the object perpendicular to the fluid flow (m²)
– v is the fluid velocity (m/s)

As the surface area (represented by the cross-sectional area A) increases, the drag force experienced by the object also increases, assuming all other factors remain constant. This is because a larger surface area provides a larger target for the fluid to act upon, resulting in a greater force being exerted on the object.

It’s important to note that the drag coefficient CD is also influenced by the object’s shape and surface roughness, as these factors can affect the flow patterns and boundary layer behavior around the object.

Examples and Applications

Example 1: Fluid Friction on a Sphere

Consider a smooth, spherical object with a diameter of 10 cm (0.1 m) moving through water at a velocity of 2 m/s. The density of water is 1000 kg/m³, and the dynamic viscosity of water is 0.001 Pa·s.

1. Calculate the Reynolds number:
   NR = ρ0 v L / η
NR = (1000 kg/m³) × (2 m/s) × (0.1 m) / (0.001 Pa·s)
NR = 20,000
   This high Reynolds number indicates that the flow is dominated by inertial forces, and the fluid friction is primarily determined by the velocity and size of the object.

2. Calculate the drag force:
   Fdrag = 1/2 CD ρ0 A v²
   Assuming a drag coefficient of 0.47 for a smooth sphere at this Reynolds number, the drag force can be calculated as:
   Fdrag = 1/2 × 0.47 × (1000 kg/m³) × (π × (0.1 m)²/4) × (2 m/s)²
Fdrag = 2.35 N
   The drag force experienced by the spherical object is 2.35 N.

Example 2: Fluid Friction on a Cylinder

Consider a cylindrical object with a diameter of 5 cm (0.05 m) and a length of 20 cm (0.2 m) moving through air at a velocity of 10 m/s. The density of air is 1.225 kg/m³, and the dynamic viscosity of air is 0.00001 Pa·s.

1. Calculate the Reynolds number:
   NR = ρ0 v L / η
NR = (1.225 kg/m³) × (10 m/s) × (0.05 m) / (0.00001 Pa·s)
NR = 61,250
   This high Reynolds number indicates that the flow is dominated by inertial forces, and the fluid friction is primarily determined by the velocity and size of the object.

2. Calculate the drag force:
   Fdrag = 1/2 CD ρ0 A v²
   Assuming a drag coefficient of 1.2 for a smooth cylinder at this Reynolds number, the drag force can be calculated as:
   Fdrag = 1/2 × 1.2 × (1.225 kg/m³) × (π × 0.05 m × 0.2 m) × (10 m/s)²
Fdrag = 14.7 N
   The drag force experienced by the cylindrical object is 14.7 N.

These examples demonstrate how the Reynolds number and the drag force equation can be used to quantify the fluid friction experienced by objects with different shapes and sizes moving through fluids.

Factors Affecting Fluid Friction and Surface Area

In addition to the factors mentioned earlier, there are several other parameters that can influence the relationship between fluid friction and surface area:

1. Fluid Compressibility: For high-speed flows, the compressibility of the fluid can become significant, affecting the fluid friction and the drag force.
2. Boundary Layer Behavior: The development and behavior of the boundary layer around the object can significantly impact the fluid friction, especially at high Reynolds numbers.
3. Surface Roughness and Texture: Rougher surfaces or textured surfaces can alter the boundary layer behavior and the flow patterns, leading to changes in fluid friction.
4. Object Orientation: The orientation of the object relative to the fluid flow can affect the effective surface area and the drag coefficient, impacting the fluid friction.
5. Fluid Turbulence: Turbulent fluid flow can introduce additional complexities in the fluid friction analysis, requiring more advanced modeling techniques.

Understanding these factors and their influence on fluid friction and surface area is crucial for designing efficient systems, optimizing fluid flow, and predicting the performance of various engineering applications.

Conclusion

Fluid friction and surface area are closely related concepts in physics, with the surface area of an object immersed in a fluid directly affecting the amount of fluid friction it experiences. By understanding the principles of fluid friction, the Reynolds number, and the drag force equation, you can effectively analyze and quantify the fluid friction experienced by objects of different shapes and sizes moving through various fluids.

This comprehensive guide has provided you with the necessary tools and knowledge to delve deeper into the intricacies of fluid friction and surface area, equipping you with the skills to tackle complex problems and design efficient systems in various fields, from aerodynamics to fluid dynamics.

References

1. Fluid Friction – Law, Examples, Types, Factors Affecting and Solved Problems. (n.d.). Vedantu. https://www.vedantu.com/physics/fluid-friction
2. Fluid Friction and Surface Area. (n.d.). The Physics Classroom. https://www.physicsclassroom.com/class/fluids/Lesson-4/Fluid-Friction-and-Surface-Area
3. Reynolds Number. (n.d.). Encyclopædia Britannica. https://www.britannica.com/science/Reynolds-number
4. Fluid Mechanics. (n.d.). Khan Academy. https://www.khanacademy.org/science/physics/fluids
5. Fluid Dynamics. (n.d.). MIT OpenCourseWare. https://ocw.mit.edu/courses/aeronautics-and-astronautics/16-01-unified-engineering-i-ii-iii-iv-fall-2005-spring-2006/fluid-dynamics/