How To Calculate Volume Flow Rate: From Several Entities, Problem Examples


 “How to calculate Volume Flow Rate of a fluid?” is one of the most frequently faced question in an chemical industry for the smooth, safe and cost effective running of a process.

The movement of fluids through a pipe in an engineering plant has great importance especially to ensure the correct proportion of different chemicals for a reaction. Calculation of Volume Flow Rate from different entities play a major role.

Volumetric Flow Rate is the volume of a fluid flows through a tube, duct, channel or other this type of structure per unit time.

Volume Flow Rate, Q or V=Av

Where A= Cross sectional area of a section in m2

And      v=Average velocity of the fluid throughout the section in m/s.

The unit of Volume Flow Rate is m3/s(cubic meters/second), m3/h(cubic meter/hour), l/s (litre/second), l/min.(litre/minute),ml/s(millilitre/second) etc.

In case of very small flow rate(for example fluid inside a syringe), ml/s is preferred and for very large volume flow rate(for example flow of water in a river), it is expressed in m3/h.

How to calculate Volume Flow Rate from Volume and Time?

Volume Flow Rate is a common term associated with flow measurement especially in case of liquids and gases.

 To calculate Volume Flow Rate of a fluid using the amount of fluid passing through (in cubic meter)a passage within a particular time period (in second), we can use the following formula:

Volume Flow Rate, Q=V/t

 

Volume Flow Rate of  a fluid (gas and liquid)is the volume of fluid passing a given point within a given period of time. Units are litre/minute, cubic centimetres per minute etc. It is denoted by Q or  

Here Volume of the Fluid =A.d

A is cross sectional area of the pipe in m2 and d is the distance traveled by the fluid in m

Q= Volume flow rate m3/s or L/s .

V=Volume of fluid in litre or cubic metre

=Average velocity of flow in m/s

Here we consider the average value of the velocity because due to frictional force velocity is less near the wall of the pipe than at the middle portion.

A=Cross sectional area occupied by the moving fluid m2

Hence,

How to find Volume Flow Rate with Pressure?

For the movement of a fluid through a duct there should be a pressure difference in between the two ends of the duct, which is termed as pressure gradient .

Hagen Poiseuille equation gives the relationship between pressure drop and flow rate of a fluid through a long cylindrical pipe. The equation is applied for laminar flow of incompressible liquid flowing through a pipe of constant cross sectional area.

If we consider two points in the flow path and observe the pressures, a vast difference of pressure results a higher mass flow rate and vice versa.

The transportation of fluid through a pipe is due to the pressure differences, the fluid is forced from a high pressure point to a low pressure point.

The Poiseuille’s Law formula is given by

Where \Delta p is   the pressure difference between the two ends of the pipe

L is the length of pipe,

μ is the dynamic viscosity,

is the volumetric flow rate,

R is the pipe radius,

A is the cross section of pipe.

From Eq(1)

Using Eq(2) we can determine the Volume Flow Rate from Pressure Gradient.

One of the common application of Hagen–Poiseuille equation( or Hagen–Poiseuille law)is observed in flow of liquid through a drinking straw. Here pressure drop is considered due to viscosity of the fluid.

In case of incompressible fluids like water we can apply Bernoulli’s equation to know the relationship between fluid flow and pressure. Here, fluid velocity of incompressible nonviscous flow is determined from the pressure measurements.  

Flow through a pipe with different cross section

Mathematically, Bernoulli’s principle can be given as-

P = pressure

v = velocity

ρ = density of the fluid

g = gravity

h = height

How to find Volume Flow Rate without Velocity?

Volume Flow Rate is a common term associated with flow measurement especially in case of liquids and gases.

The equation to find Volume Flow Rate of a fluid without knowing its velocity is as follows:

Q=V/t

Where Q=Volume Flow Rate m3/s

V = Volume of the fluid passing through a particular cross sectional area in m3

t =Time taken by the fluid second

how to calculate volume flow rate
Volume Flow Rate

In the above figure, a fluid is passing through a duct, if V is the Volume of fluid crossed a unit cross sectional area A of the pipe within a time period of ‘t’, then Volume Flow Rate Q is given by

Q=V/t

How to calculate Volume Flow Rate of air?

Different types of devices are used to measure the Volume Flow Rate of a fluid depending upon its precision in measurement and its price in the market.

 To calculate Volume Flow Rate of air we can use the following formula:

Q=Cross sectional area x Average velocity

Generally air velocity i.e. distance traveled by air per unit time is represented in feet per minute is not uniform at each portion of the duct.

The air velocity is lowest near the walls of the duct due to friction, considering this we can use an averaging Pitot tube having several number of sensing points to get average velocity more precisely.

If the dimension of the duct is known to us then we can easily calculate the cross sectional area of the duct and then multiplying it with average velocity, we can determine the Volume Flow rate, generally in cubic feet per minute.

The following devices measure volumetric flow:

How to calculate Volume Flow Rate of Water?

The amount of water flowing through a duct or pipe within a particular time period which is known as Volume Flow Rate can be calculated using the following equation:

 Q=Cross sectional area x Average velocity

Here we consider the average velocity of water since the speed of water is not uniform through out the whole pipe, speed is maximum at the centre of the pipe and minimum near the side portion.

Different types of Flow measuring devices are used, most of them follow the Bernoulli’s theorem to determine the velocity of flow depending on the pressure gradient between two points in the passage of the fluid.

Venturimeter;Image Credit: wikipedia

To know more about Volume Flow rate(click here)

Problem1:Water is flowing through a pipe of inner radius 10 cm with a volume flow rate of 0.50 m3/s. Calculate the speed of water through the pipe.

Solution: Data given are:

Radius of the pipe, r=10 cm=0.1m

Volume Flow Rate, Q=0.50m3/s

Now area of the pipe,A= πr2=3.14 x 0.01=0.0314m2

We know that,Q=v.A

Here v is the speed or velocity of water in m/s

Speed of water,v=Q/A=0.50/0.0314=15.92 m/s

Problem2: A nozzle with a radius of 0.150 cm is attached to a garden hose with a radius of 0.700 cm. The flow rate through hose and nozzle is 0.500 L/s. Determine the velocity of the water (a) in the hose and (b) in the nozzle.

Solution:

(a) velocity of the water in the hose

 We know that,Q=v.A

Radius of the hose,r1=0.700cm=0.007m

Area of the hose A1=πr2=3.14 x 0.000049=.00015m2

Flow Rate,Q=0.500 L/s=0.0005 m3/s

Therefore the velocity of water in the hose,v1=Q/A1=.0005/.00015=3.33m/s

(b) velocity of the water in the nozzle.

Radius of the nozzle,r2=.150cm=.0015m

We know from Equation of Continuity,A1v1=A2v2

Hence,

    Now,

Sangeeta Das

I am Sangeeta Das. I have completed my Masters in Mechanical Engineering with specialization in I.C Engine and Automobiles. I have around ten years of experience encompassing industry and academia. My area of interest includes I.C. Engines, Aerodynamics and Fluid Mechanics. You can reach me at https://www.linkedin.com/in/sangeeta-das-57233a203/

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