Calculation of Volume for 1 hr of pumping process

I do not fully understand your question.

The relation between inlet/outlet temperature is a factor of your pump efficiency , as well as a few other details.

Maybe someone else around here with a keen sense of something I'm not aware of can help out, otherwise I'll need to ask for a bit more information.

Sorry If I'm just being dense... I've already begun to check out on this beautiful friday... I should be fishing.

Sorry, it is not possible to understand your question as posted. Please, reformulate it.

BTW, for usual thermodynamics in the current world, while pumping water, there's no appreciable temperature difference or variation in pressure due to temperature changes. You have the pump performance curve, and hopefully be happy with it.

You have to reframe the question more specifically. As Guru mentioned there will be no appreciable temp change during pumping. For any flow rate calculations we use Q= A X V where A is the area of the pipe and v is the velocity and Q is the flow rate.

Thank you all for your interest.......i try to reformulate my question in a better way with some background

I am designing a Test Rig which can generate characteristic curves to find the efficiency of Pumps and Pumps used as Turbines and considerable temperature of water arise due to 1 hr of pumping process. The temperature rises would approximately be 5 Degree and the limitation for temperature change is also 5 degree for this project.

So the mystery is how to calculate the volume the tank needed for 1 hr pumping at flow rate 500m3/hr and change in temp 5 degree celcius

what would be the dimensions of the tank?

and the fluid obviously is water

I guess you could find the cubical expansion rate of the water and this will give you the apparent increase in volume of the water that is pumped in 1 hour.

I think that the cubical expansion rate of water is 0,00018m³/m^{3 0}C

Simplified with a volume of 500m³ and a temperature difference of 5⁰C this would be

Apparent increase in volume 0.00018 x 500 x 5 = 0.45m³ or 450 litres

Don't know whether that will be of any assistance.

Ah! All right.

You have your volume flow, which may also translated to mass flow easily. Consider constant to make calculations easier, you need not to be that carefull.

You have your heat input. You already mentioned, a 5 degree delta-T for that flow.

Use the equation Q=mcDT expressing Q and m as mass flows.

But, after all, you have a pump that operates at 500 m3/h and induces a dT of 5 degC transmitted to the water. So, to keep water temp within 5 degC over one hour, you need, at least, 500 m3. Makes sense?

Thats a lot of water. Have you considered installing a heat exchanger? May be a simple one, made of tubes and cooled by natural convection. If it is a test rig, ic could benefit from it. Or, if your budget allows, go for a cooling tower, like everyone else in the world! This, associated with a bypass temp control valve, will make your pump inlet temp rest within values tighter than your 5 degs.

Hello bhrescobar - I don't think he's saying it heats 5° on one pass through the pump. See my #7. For the example I gave - 10 bar ΔP, 65% efficiency, temperature rise acroos the pump and downstream throttle is about 0.37°C.

Cheers........Codey

It's not a mystery, it's a question of applied science .

It depends on the pump differential pressure and efficiency. Rate of heat dissipation into the water = flow x head/efficiency (need to use the right units of course, but I assume you can handle that). All the pump shaft power ultimately goes into heat in the water, as you will be throttling to give the test pressure before returning to the tank.

Calculate heat input in one hour. Calculate heat per m³ to raise water by 5°C (21 MJ since you ask). Divide one by the other and you have volume.

Did an example assuming pump ΔP 10 bar (quite a decent pressure) and efficiency 65% and got about 37 m³. Motor rating at least 225 kW.

Cheers.........Codey

Temperature compensated flow meter is required for test rig.

Why? All the OP wants to know is the volume of water to limit temp rise. If he has, say an orifice meter the difference in reading between starting temp and 5°C higher (for a given actual flow) is insignificant for the pump test, let alone estimation of water volume.

Cheers..........Codey