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- Pressure Rise Through Impeller of Centrifugal Pump - Derivation & Equations

# Pressure Rise Through Impeller of Centrifugal Pump - Derivation & Equations

Learn how to calculate the pressure rise through an impeller of a centrifugal pump by deriving equations using Bernoulli's equations at the inlet and outlet of the impeller. Understand the process and principles of pressure increase through the impeller.

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## Video Transcript

Hi, Professor Vishal Taylor, welcome to my YouTube channel.

In this video, I teach you the derivation of pressure rise through impeller of centrifugal

pump.

Means, how amount of the pressure is increased by an impeller of a centrifugal pump.

So in this case, we are deriving the equations by applying the Bernoulli's equations at the

inlet and outlet of the impellers.

So, this equation is correct.

Bernoulli's equations we are required a two section that is a section 1 and

section 2 so we are giving the section 1 at the inlet of this impeller okay this

is our center of the impeller from where the water is coming from suction pipe

then water is displaced this distance this is the inlet of impeller this is

the impeller van and at the outlet we give the section 2 okay so this is a two

sections where we applying the Bernoulli's equations so at the inlet of

is impeller that is

the water or increase the pressure of the water means the pressure is increased at the

section 2 that is a P2 pressure and inlet of the pump that is a P1 pressure.

So in this case we are finding the P2 minus P1 because it is a pressure rise so we are

find out the P2 upon P1.

So what is the energy at the input so water have 8 three types of energy kinetic energy

potential energy as well as the pressure energy that we all know.

So what is the equations at the inlet.

So inlet pressure is

equal to work output. So, at the output only hydraulic energy means at the outlet water

and water contain the hydraulic energy. So, water have three forms pressure energy, velocity

energy and potential energy. So, at the section 2, so pressure is P2. So, pressure head is

P2 upon rho g plus velocity V2. So, velocity head is V2 square upon 2g plus potential energy

that is Z2. So, this is the basic equation from that we derive this equation.

So, we writing this equation in the form of p2 minus p1 upon rho g.

So, p2 minus p1 because p2 is higher and p1 is smaller.

So, this p1 upon rho g is supply on the right side and the right side another parameter

is going on to this left side.

So, this equation is written like this way p2 minus p1 upon rho g.

And another parameter is V1 square upon 2g plus Vw2 into U2 upon g and this V2 square

equations, we put the value of V2 and Vw2 from these velocity triangles.

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So here I mentioned, from the outlet velocity triangle, we have tried to find out the value

of Vw2 and V2.

opposite sides upon adjacent side. Opposite side is Vf2 this one and adjacent side is

the U2 minus Vw2. So, this equation is written. Then after from this equation is further simplified

and we write down the equation of Vw2. So, Vw2 is equal to U2 minus Vf2 into cot beta

2 means this step is going on the left side and tan beta 2 is coming in the right side.

So, it is a one way.

of hypotenuse is equal to square of both the side. So, it is V2 square is equal to both

the side means Vw2 is one side and another side is the Vf2. So, this is Pythagoras equation.

Now in this equation, we are applying or putting this value of Vw2. What is the Vw2? That we

already derived the Vw2 is equal to u2 minus Vf2 cot beta 2. So, this is the equation of

V2. And it is further simplified below.

minus 2 into first step u2 into second step vf2 cot beta2.

So, this distribution takes place then remaining is the vf2 square.

## Video Summary & Chapters

##### No chapters for this video generated yet.

## Video Transcript

Hi, Professor Vishal Taylor, welcome to my YouTube channel.

In this video, I teach you the derivation of pressure rise through impeller of centrifugal

pump.

Means, how amount of the pressure is increased by an impeller of a centrifugal pump.

So in this case, we are deriving the equations by applying the Bernoulli's equations at the

inlet and outlet of the impellers.

So, this equation is totally derived by using this velocity diagrams of a centrifugal pump.

So for that, you at least know the how to draw velocity diagrams.

And if you don't know how to draw the velocity diagrams for a centrifugal pump, then I request

you to watch my video on a velocity diagram and work done of a centrifugal pump from the

playlist.

The link is also available in the description and also from the top right screen of your

mobile from the iSymbols.

Now, for applying the...

Bernoulli's equations we are required a two section that is a section 1 and

section 2 so we are giving the section 1 at the inlet of this impeller okay this

is our center of the impeller from where the water is coming from suction pipe

then water is displaced this distance this is the inlet of impeller this is

the impeller van and at the outlet we give the section 2 okay so this is a two

sections where we applying the Bernoulli's equations so at the inlet of

this impeller there are two things available. First one is the energy in the water at the

section 1 plus work done supplied by the impeller. And at the outlet there is only one thing

that is the water available at the section 2 means energy at the section 2. So, we are

writing that energy at the input plus work input by this impeller is equal to total work

output. This work output is in the form of water. So, we generally know the pump is used

the water or increase the pressure of the water means the pressure is increased at the

section 2 that is a P2 pressure and inlet of the pump that is a P1 pressure.

So in this case we are finding the P2 minus P1 because it is a pressure rise.

So we are find out the P2 upon P1.

So what is the energy at the input?

So water have 8 three types of energy kinetic energy, potential energy as well as the pressure

energy that we all know.

Okay, so what is the equations at the inlet?

So, inlet pressure is P1 upon rho g is known as the pressure energy plus velocity energy

velocity at the section 1 is the V1.

So, velocity energy is V1 square by 2g and the potential energy it is a Z1.

Plus work input by the impeller that is a work input by the impeller is the Vw2 into

U2 by g.

So, that we already discussed in a work done of centrifugal pump.

So, you can watch the Wordmem by Pom from the description or playlist for all the i

symbols.

Easy.

equal to work output. So, at the output only hydraulic energy means at the outlet water

and water contain the hydraulic energy. So, water have three forms pressure energy, velocity

energy and potential energy. So, at the section 2, so pressure is P2. So, pressure head is

P2 upon rho g plus velocity V2. So, velocity head is V2 square upon 2g plus potential energy

that is Z2. So, this is the basic equation from that we derive this equation.

Now, we consider that or we assume that z1 and z2 are equal because this impeller width

is negligible, that is a very small.

So, we have considered z1 is equal to z2.