If I have understand your question clearly then following solution might help you.

PFA

Good luck for your research!

Regards

Naveen

Hi Mahdieh,

in the simple case, where you do not consider friction in the tube, the stagnation pressure will be equal to the dynamic pressure. If you want to consider friction, you will need to find out, if the flow regime and the the discarge coefficient. Once you have the answers, you can simply calculate the stagnation pressure by the Darcy-Weisbach equation, see here (unfortunately in German):

https://de.wikipedia.org/wiki/Druckverlust

Good luck!

Best regards,

Antoni Artinov

What else is given? The flow rate at the entry of the first tube ?

As said above, the stagnation pressure is equal to the total pressure of the water jet, which is simply dynamic pressure plus ambient pressure. And dynamic pressure is rho/2 * v^2.

@Naveen Mani Tripathi

Thanks alot for the answer, that totally make sense.

@Antoni Artinov:

Thank you so much, yes I have calculated the friction and pressure loss. My main problem was:

1. can I find the stagnation pressure by deducting the pressure loss from dynamic pressure?

2. I can provide a constant flow rate by the pump so v = q/A

3. does jet kinetic energy decreases as it goes forward?

@Nils Beck

I can provide a constant flow rate with the pump

@Naveen Mani Tripathi

Is P1 the same as the pressure that I can read at pump side?

@Mahdieh

Yes, it is initial pressure. If nothing else (valve etc.) is connected between pipe and pump then P1 will be pressure at pump side. Otherwise, you have to reduce the pressure drop due valve from the pump side pressure.

I hope it is clear to you.

--

Regards

Naveen

@Naveen Mani Tripathi

Thank you very much for your time. My pump can only provide flow rate so the pressure that I got is a function of the flow rate. For each flow rate depending on my configuration in front of it I can get a specific pressure.

Thank you alot! It helps me understand it clearly!

The pressure losses in the pipes are actually irrelevant. If you know your flow rate and the diameter of the last pipe at the outlet, you can calculate your jet velocity and from that the dynamic pressure. Once the jet has left the pipe, it's static pressure will be equal to ambient pressure. An total = stagnation = static+dynamic.

@Nils Beck thatnks Nils, that makes a lot of sense to me now!