Power Calculation for Scaled Pump Model

[GBA13]

Homework Statement

Hi Guys,

I have this question:
b. A model scaled to one-third the size of the prototype has the following characteristics:
Omegam = 900 rpm
Dm = 5 in
deltaHm = 10 ft
Qm = 3 ft^3/s
Pm = 2 hp
If the full-size pump is to run at 300 rpm, what is the power required for this pump?

Homework Equations

I have found the non dimensional form as:

P/rho * omega^3 * D^5 = f(deltaH/D, Q/Omega * D^3)

density of the fluid, rho
angular speed of the rotor, omega
diameter of the rotor, D
head rise across the pump, deltaH
volumetric flow through the pump, Q

The Attempt at a Solution

[/B]
I'm really not sure where to start, I thought I could equate the model equation, P/rho * omega^3 * D^5 with the real life size version but I don't have enough data to rearrange it and am very confused. Could you guys please offer a hand? The answer is 18.

Thanks!

 

[RUber]

I think that you should start with what you thought you could start with.

The Attempt at a Solution

[/B]
I'm really not sure where to start, I thought I could equate the model equation, P/rho * omega^3 * D^5 with the real life size version but I don't have enough data to rearrange it and am very confused. Could you guys please offer a hand? The answer is 18.

What things are different between the model and the full-size version? P, D and omega.
Write the full-size version in terms of the model parameters.

 

[GBA13]

I think that you should start with what you thought you could start with.What things are different between the model and the full-size version? P, D and omega.
Write the full-size version in terms of the model parameters.

The problem is that I've posted everything I've been told. Normally it would be quite an easy question but I swear I'm not given enough information. I'll Include a screen shot of the problem.

 

[Chestermiller]

I'm confused. You obtained the correct functional relationship. Is it that you are having a problem with the actual scaling? What would it take to hold the two dimensionless groups in the right hand side of the equation constant, in terms of the required changes in Q and delta H? What would it take to hold the dimensionless group on the left hand side of the equation constant in terms of the change in P?

Chet

 

[GBA13]

I'm confused. You obtained the correct functional relationship. Is it that you are having a problem with the actual scaling? What would it take to hold the two dimensionless groups in the right hand side of the equation constant, in terms of the required changes in Q and delta H? What would it take to hold the dimensionless group on the left hand side of the equation constant in terms of the change in P?

Chet

Hi Chet,

Yes it is the scaling which I'm stuck on. As I'm quite new to this I have only done questions where you work out the functional relationship and then equate one side of it with itself and plug in the numbers they give you for the model and full size versions and then rearrange for the unknown. As there is two extra pi groups in this case I'm just not sure what I should be doing.

 

[Chestermiller]

Hi Chet,

Yes it is the scaling which I'm stuck on. As I'm quite new to this I have only done questions where you work out the functional relationship and then equate one side of it with itself and plug in the numbers they give you for the model and full size versions and then rearrange for the unknown. As there is two extra pi groups in this case I'm just not sure what I should be doing.

You need to find the changes you need to have in Q, P, and delta H to hold the three dimensionless groups the same as in the scale model case. You have 3 groups and 3 parameters to play with.

Chet

 

[GBA13]

Ok I get it, I just got them all right! Thanks very much for your help! :)