How To Calculate Pressure Difference: What, How, Examples


“How to calculate pressure difference?”, in this article we will try to find the answer for this question. Also we will discuss about different pressure difference measuring devices.

Pressure difference also known as pressure gradient or differential pressure is the difference between two measured pressure values or it is the comparison of two arbitrary pressures.

Pressure difference is calculated in different industries in day to day basis for flow and filtration of various fluids through pipelines.

Pressure difference or differential pressure ΔP is the difference between any two applied pressures, generally all pressure readings can be assumed as differential reading as, in case of absolute pressure, in relation to vacuum pressure and gauge pressure in relation to atmospheric pressure.

Water Pressure; Image Credit:unsplash
High Pressure Pipe Leaking; Image Credit:unsplash

What Is Pressure?

In simple word, pressure is the force exerted over a given area.

Pressure is defined as the force per unit area.

Pressure=Force/Area

Where Force(F) is in Newton

And Area(A) is in meter2

Therefore Pressure,p=F/A Newton/metre2 or Pascal.

 Pressure increases as we move down from the liquid surface, the pressure is always greater for denser medium. Manometer and Barometer are the measuring instruments used to measure pressure.

how to calculate pressure difference
Pressure as exerted by particle collisions inside a closed container; Image Credit:wikipedia
Pressure=Force/Area; Image Credit: wikipedia

What is Pressure Difference?

Pressure Difference is calculated in regular intervals or continuously in different industries like chemical plants, refineries, petrochemical plants etc.

Pressure Difference is the difference between pressures when they are measured in different points. Pressure Difference calculations are done regularly in various industries for flow and level measurement of fluids, filter monitoring and clog detection. Pressure difference is measures in Pound per Square Inch(PSI).

This simple concept of pressure difference acts as a vital concept in process industries because it is responsible for the flow of a fluid from one point to another. Pressurization of airplane cabins is one of the most appreciated application of Pressure Difference.

Pressure device for industry system; Image Credit:unsplash

Pressure Difference is continuously monitored in industries to know whether there is any clog or contaminates through a pipeline.

If a part of a pipeline gets clogged, there is a change in pressure which makes a change in Pressure Difference, an operator can easily detect the exact blockage point and clean the pipeline to ensure the smooth flow of the fluid.

For a maximum value of pressure difference, we may have to change the filter otherwise it may lead to damage or corrosion.

To determine the respiratory flow in medical devices, air flow blockages in different devices, clogged filter detection in extractor fans, air conditioner, exhaust ducts are the examples of applications where Pressure difference monitoring plays an important role.

Hydrostatic Pressure Difference

Hydrostatic Pressure Difference is specific measurement of liquid pressure above a vertical datum at different points or at different heights from the datum line.

The pressure of a liquid at rest at a certain depth due to gravitational force is known as Hydrostatic Pressure and hydrostatic pressure increases as the depth measured from the surface increases because of the increasing weight of the fluid exerts more downward force on the lower liquid layers.

Hydrostatic Pressure at different depths; Image Credit: wikipedia

The formula used to calculate hydrostatic pressure is shown below:

p=ρgh

Where,

P is the pressure exerted by the liquid in Nm-2

ρ is the density of the liquid in kgm-3

g is the acceleration due to gravity considered as 9.81 ms-2

h is the height of the fluid column in ‘m’

A swimmer experiences more pressure as he goes deeper underwater because of the more and more weight on the top as well as the air above him.

How to Calculate Pressure Difference?

.Differential Pressure Gauges and Differential U-tube Manometer are used to calculate the pressure difference between two points of same liquid or different liquids.

Differential pressure gauges consists of two inlet ports, each port is connected to one of the pipes or sources whose pressure is to be monitored.

U tube manometer is a device used to measure the pressure difference between two points which may be in the same pipe or in two different pipes. As the name suggest it looks like the alphabet U, the bottom portion of the glass tube is filled with heavy liquid like mercury, water and air are also used as per requirement.

Differential Mercury Manometer; Image Credit:wikipedia
A pressure gauge in action ; Image Credit:wikipedia

Differential Pressure gauge performs the mathematical operation of subtraction through mechanical means, If there is a pressure difference in both the pipes or sources, the pressure exerted on one measuring element is more than the pressure exerted on another chamber element,then the Differential Pressure gauge shows deflection.

How to Calculate Pressure Difference in Manometer?

Pressure Difference between two pipes or sources is calculated by using Differential U-type Manometer.

A Differential manometer is a device used to compare the pressures in two different pipes or containers from the vertical distance from the surface of a liquid in two limbs when each of the limbs are connected to two different sources.

U-tube Manometer; Image credit: wikipedia

To determine the difference in pressure, multiply the difference in height by the density of the fluid and the acceleration due to gravity. The final units should be in pascals.

How to Calculate flow rate from pressure difference?

Bernoulli’s Equation gives a relationship between the Pressure Difference and the Flow of a fluid, using this relation we can easily calculate the amount of fluid flowing within a time interval.

The Bernoulli’s Principle applicable for incompressible fluids(with negligible viscosity) states that an increase in a speed of a fluid moving in a streamline occurs with a decrease in static pressure of the fluid. In simple words, static pressure+ dynamic pressure=total pressure which is constant.

Flow of fluid through a venturimeter; Image Credit:wikipedia
Flow of fluid through a venturimeter; Image Credit:wikipedia

Bernoulli’s Principle can be expressed in terms of a mathematical formula as below:

Where v=fluid speed

g = acceleration due to gravity considered as 9.81 m.s-2

y=height above datum line

p=pressure of the fluid

ρ = density of the fluid

Now considering any two points in the liquid,

Now g is same at both the points,

Since the fluid is considered as incompressible,

From Continuity Equation, v1A1 = v2A2

From Eq(2),

From Eq(3) we can calculate flow rate(Q=Area x average velocity) through the duct using pressure difference p1 – p2

Measurement of amount of fluid flows within a time interval is quite important in a process industry for the smooth and safe running of different operations.

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.

Where Δp 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.

How to Calculate Pressure Difference in Venturi meter?

A venturimeter is a type of flow meter where volumetric flow rate of a fluid is determined on the basis of Bernoulli’s theorem.

When a fluid passes through a venturimeter, it accelerates in the convergent part and then decelerates in the divergent part. The pressure of fluid is different throughout the venturimeter and the Pressure Difference is obtained from the Manometer reading. Using this estimated pressure difference and applying Bernoulli’s equation and Continuity equation, volumetric flow rate is calculated.

how to calculate pressure difference
Venturimeter; Image Credit: wikipedia
Venturimeter; Image Credit: wikipedia

To know about Flow Rate(click here)

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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