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# Flow rate, Pressure rise and Power calculations. Fluid Mechanics

## Question

A large pump delivering 1.2 m3/s of water with a pressure rise of 400 kPa is needed for a particular hydroelectric power plant. A proposed design change is tested on a smaller 1:4 scale pump. Estimate the flow rate and pressure rise which would be expected in the model study. If the power needed to operate the model pump is measured to be 8000 kW, what power would be expected to operate the prototype pump?

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Good afternoon nwankotiwk

the problem you show is very interesting, but from yesterdey I made my calculations, I was not very sure about the values I had, I made one more time the calculations with the values of 1.2 m3/s and 400 kPa, but I have the power of the motor smaller than you show, I have 478 KW or 661 HP, I made it with a short calculation yesterday and today with the Crane flow of fluids. And with the problem I will calculate the size of the motor with a quarter of flow and a quarter of the pressure, cuold you please give me an answer. thanks, i write from Mexico City.

Felipe Romero.

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I would like to know hte background of this question prior to offer any assistance...

...whilst more than happy to help, it sounds a little too-much like a college/univeristy homework question!

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On 14/03/2016 at 10:49 AM, nwankotiwk said:

Well, if I did the correct calculations, you'll need a power about 408 kW to the main pump. And, with a quarter of the size from the main pump, you're going to have a quarter of the flow rate, possibly, the pressure can be higher than the main pump (More flow rate less pressure. Less flow rate more pressure). Them, you have 18000 L/min. If you want to know what maximun pressure you can have with 8000 kW without damaging the eletric motor, then it would be about 313 bar (31300 kPa). It'll be possible considering a 0,85 as Hydraulic pump rate.

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Thanks for all the reply guys.

There are no actual answers for this question. It is a real life practical exercise taking place in the Gold Mine where I am currently working as a Junior Engineer. All I need is a precise algorithm and approach towards solving this problem. My Senior Engineer intends building a model of this system from the findings, elaborative engineering reasons on assumptions made where necessary. Hence I genuinely seek advices from you guys as my Engineering Family.

I intentionally didn't put plenty of information in my question and had to keep it straight and simple. I used hydroelectric power plant for simplicity than a Gold Mine, however, let me go deep a little bit to the actual scenario as it stands.

We used to have a pumping system from the bottom level C to upper level A which is roughly 40.8m high. At level B in between C&A there is a dam with which it’s fed with water from level A. The water gravitates from Level A to Level B to run the Pelton Turbine to generate back-up power. From the history of this system, the water that was flowing out of the dam was at 1.2m3/s.

Logically to me, I thought, for the dam level to remain constant then the volume of water entering the dam per second must be the same as the volume of water exiting the dam. That’s where I got the pumps delivery flow rate of 1.2m^3/s . With the head of 40.8m, assuming the density of water to be 1000kg/m^3 and gravity at 9.8 m/s^2 I got the Pressure=) to be 400kPa.

I thought scaling down the actual parameters at 1:4 is ideal and feasible for model study purposes.

My understanding:

ûThe only thing that relates the prototype pump to the model pump is the scale of 1:4

ûThe modification "Design Change" only applies on the pump and what is directly linked to it, nothing else.

ûThe flow rate for model study must be one quarter of the actual flow rate and is 0.3m^3/s

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I undertand. I worked with hydraulics equippments from the ships like cranes, cylinders, valves etc. This king of hydraulics We use mineral oil, but, I think you also should know the pressure that you'll have when the pump is running, because the tubes will make a little bit of restriction which can increase the pressure. In a few thrusters systems We have this oil column, and when We turn on the system, the pressure increase a little bit. In my hydraulic area, normally, when we have a small size of pump, the pressure can be highier than a big one, and the power to make it run can be small too. I suggest to descover the calculate the loss charge in all the circuit to be sure that you won't have any trouble in your electrical motor. I used to use this formula.
Sorry, because it's in Portuguese. I'm talking from Brazil. =D

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