In this article, we will discuss the velocity triangle or velocity diagram of the centrifugal pump along with the basics, how to draw it and work done of a centrifugal pump.
As the name suggests, a velocity triangle or velocity diagram is basically a triangle indicating different components of velocities.
It is used to reflect the velocities mainly in turbomachinery like,
Here, we will discuss the velocity triangle of centrifugal pump!
We already learned that working fluid is undergoing various processes and it has different velocities due to different kinds of movements. In the centrifugal pump, due to radial intake as well as the rotation of the impeller, three types of velocities will be introduced,
Let’s learn the basics of these velocities, to have a clear idea first!
If any object is moving along a circular path, the linear velocity component across the periphery is called tangential velocity.
It means the velocity of fluids with respect to the surrounding as well as the stationary environment.
It is simply defined as the resultant of two or more velocities. Here, the resultant of tangential velocity and absolute velocity is called resultant velocity.
It is normally denoted by Vr.
Let’s understand it with a very simple concept! To calculate the work done, by a centrifugal pump, we must know the velocity triangle!
The impeller is rotating, within the centrifugal pump casing.
If we observe the impeller, we understand that an impeller is consisting of many blades. The blade arrangement in the impeller may be of different based on the types of impellers.
To illustrate the centrifugal pump velocity triangle, we will take only one single blade for diagram.
Look at this blade, it has two radius,
The Centre of the impeller is indicated as ‘O’.
We have seen that water enters the centrifugal pump radially. We need to introduce three velocity terms,
Let’s consider, the pump is working and fluid, say, water enters into the pump inlet. Water has asked a has 2m/s at the inlet of the pump.
Now, let me ask you a question,
Let me explain, here water has some velocity, and simultaneously the impeller has also some velocity, hence, the water will not enter with the same velocity.
It will increase and that depends on the impeller speed and this change will be applicable at the inlet and outlet both.
So, the velocity of water which is supposed to enter at the inlet if the impeller is not rotating, is known as absolute velocity.
The impeller rotates, so naturally, the blade also rotates. Consider, the angular velocity of the blade is ω.
Due to this angular velocity, there will be tangential velocity at inlet and outlet peripherals of the impeller. So, water will get two different kinds of velocity,
Refer Below to watch an ANIMATED VIDEO for Centrifugal Pump basics & Velocity Triangle!
What do you think, the water enters the blade, with absolute velocity?
No, it will be relative velocity!
Here, the resultant velocity that is nothing but the relative velocity comes into the picture. The resultant velocity of absolute and tangential velocity is actually entering and exit at the inlet and outlet respectively.
Let’s draw, absolute velocity of water, V1 at the inlet. Tangential velocity u1 and u2 also to be drawn at the inlet and outlet respectively.
Tangential velocity, u2 at the outlet is large than the tangential velocity at the inlet.
It is very easy to explain!
We all know that,
u = π DN/60
It means, u is proportional to D, if N is constant.
In our diagram,
So, it is proved that u2 > u1.
At the inlet side, we got, V1 and u1.
Here, Vr1 is the relative velocity of absolute velocity, V1 and tangential velocity, u1.
Hence, V1, u1, and Vr1 form a velocity triangle at the inlet.
From the outlet, water will exit with relative velocity, Vr2. This relative velocity, Vr2 is the resultant of the absolute velocity V2 and tangential velocity u2.
Hence, V2, u2, and Vr2 form a velocity triangle at the outlet.
Water enters radially, hence, the angle between tangential velocity, U1, and absolute velocity, V1 is 90 degree.
The absolute velocity will have two components!
As the angle is α, the horizontal component will be, V1cosα,
The Vertical component will be, V1 sinα.
As α is 90 degree, V1cosα = V1cos90 = 0,
This is nothing but the whirl velocity, Vw1 = 0
and V1 sinα = V1 sin90 = V1. This is flow velocity, hence, ‘Vf1 = V1
In the same way, at the outlet, absolute velocity V2 also will have two components,
In this way, the triangle at the outlet is completed
Angular momentum, L = Mass x tangential velocity x radius.
Angular momentum, L1 per second at inlet = m Vw1 R1
Angular momentum L2 per second at outlet = m Vw2 R2
Torque Transmitted, T
As we know, w = mg or mρQ
Work done (W.D) per second for ‘w’ weight,
We know, u = ωR, So, u1 = ωR1 and u2 = ωR2
Work done per second, for w weight of water, striking per second,
W.D = w (Vw2 u2 – Vw1 u1)/g
Work done per second, per unit weight of water, striking per second,
= (Vw2 u2 – Vw1 u1)/g [As a unit weight, then, w=1,]
Also, we have seen that, Vw1 = 0, due to radial velocity,
Hence, work done, W.D will be, Vw2 u2 /g
The internal diameter and outer diameter of a centrifugal pump impeller are 250mm and 350mm respectively. The rotational speed of impeller is 1400 RPM. 30° and 45° are the vane angle at inlet and outlet respectively.
Velocity of flow is same at both inlet and outlet and water enters radially. Find out the work done by impeller per unit weight of water.
Let’s try to solve this problem step by step in simple manner!
The data have been given in the problem, as follows:
Velocity Triangle or Diagram
As per the problem, see the velocity triangle as below,
We have got D1, D2, hence, we will get u1 and u2,
From velocity triangle at inlet,
So, we can write,
As per problem, flow velocity is same, that is Vf1 = Vf2 = 10.58 m/s
From velocity triangle at outlet,
So, we can write,
Hence, work done by impeller per unit weight,
Hence, the work done becomes 39.47 N-m/N.
Hence, we have got a very basic idea of velocity triangle or velocity diagram along with work done calculations.
Any query, please let us know.
Let’s check a few nice articles for further study,
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