Question about pressure drops due to friction and valves

[hockeyfan26]

If I'm designing an injector for a rocket engine, I have a specific mean flow rate (m/s) that must be met due to the pipe diameter and the required mass flow rate.

I've calculated all the pressure drops due to lost work from friction, valves, and orifice geometries (not from change in area, but due to the complex internal geometries that lead to losses in energy).

For calculating the necessary area of the injector plate orifices what pressure drop should I use? Should I use the pressure drop I determined to get the required flow rate or should I do this:

pressure drop over injector = (the required pressure drop to achieve the required mass flow rate ) - [(pressure drop from friction) + (pressure drop over check valves/etc)]

or this:

Pressure drop over injector = pressure drop to obtain required mean flow rate

Example: The combustion chamber is at 500 psi. I need a pressure drop of let's say 90 psi to get the required flow rate into the combustion chamber. The pressure drop from friction is 30 psi and the pressure drop from a check valve is 15 psi. For the pressure drop over the injector should I use 90psi (regulator below tank would be set to 635 psi) or 45 psi (regulator below tank would be set to 590 psi in this case)?

I guess what my question boils down to:
1) Do pressure drops due to frictional losses and losses due to flowing through valves increase the speed of the flow (or are they just considered lost energy that causes a pressure drop, but no corresponding velocity increase)?

2) As the flow of liquid/gas exits a regulator can we assume the velocity is zero at that point of our control volume, and calculate the velocity from the overall pressure drop from the regulator to the other end of the control volume?

I'm guessing that pressure drops due to friction and check valves do indeed increase flow rate since in my chemical engineering curriculum pressure gradients are generated from frictional losses and commonly used to increase volumetric flow rates in plug flow reactors. But on the other hand the increased volumetric flow rate could just be from the expansion of the reactants at the lower pressures.

I greatly appreciate any advice/help with this. Thanks!

 

[Rx7man]

Restrictions, etc would cause a pressure drop only.. flow in = flow out, so velocity wouldn't go up or down unless you're changing piping diameter... at least for liquids.. for a gas a change in pressure will come with a corresponding change in temperature and volume.

Not quite sure how to answer part 2 though.. perhaps someone else will chime in

Welcome to PF :)

 

[Nidum]

Is this a real world engineering design problem or a college project or homework or just for personal interest ?

Have you ever done courses in elementary fluid mechanics ?

 

[hockeyfan26]

Is this a real world engineering design problem or a college project or homework or just for personal interest ?

Have you ever done courses in elementary fluid mechanics ?

This is a real world engineering design problem. I'm part of a large group of engineers in their sophomore to senior years(mostly meche and aero) building a liquid engine. We meet every week to discuss calculations, we have a bunch people who all attempt the problem individually. I'm probably one of the weakest technical members, especially in fluid mechanics. Also, these are just 1st order calculations (very rough) for the plumbing system. Everything eventually gets simulated in Ansys CFD and CHEMCAD. I would like to have a better understanding of this so I can keep up with the technical discussions. This is also for personal interest because I would like to brush up on my fluid mechanics.

I took a course my freshman year about 2 years ago, but haven't really touched a lot of fluid mechanics problems since then and I'm struggling to get back into it.

Even if most of what I listed can't be explained, if someone could just provide the correct answer for the two choices I listed in the example question it would be greatly appreciated.

 

[Tom.G]

See if this helps.

 

[tkyoung75]

flow rate (m/s)

Flow rate is m3/s, flow velocity is m/s.

area of the injector plate orifices what pressure drop should I use?

As shown by Tom.G,, total pressure loss is the sum of the pressure losses across each section / component of the path.

guessing that pressure drops due to friction and check valves do indeed increase flow rate

Get a garden hose and squeeze the end or put your finger over it, bend it in half, so the flow stops, then release the flow with your finger still on it. Use a bucket to measure the flowrate Does increasing the friction increase the flow rate? flow velocity? Not only what you see, but what you can't see, in the hose.

 

[JBA]

There is a minimum pressure differential required to provide a given flow rate through a nozzle based upon the diameter of the nozzle and it flow coefficient (efficiency) and a well designed flow nozzle can have a coefficient of as high as .98 (98% of the theoretical nozzle flow).

There are two methods with which you can approach your nozzle issue:
One is to work your problem backwards starting with the expected pressure on the discharge side of the nozzle to determine the required nozzle inlet pressure to provide your required fuel flow and then add the pressure drop values of the upstream piping and components to determine the required supply pressure to provide your required fuel flow.

The other, if you already have a specific supply pressure, then is to calculate the nozzle diameter based upon attaining your required flow based upon the differential between the inlet nozzle pressure after subtracting your upstream losses and the expected downstream nozzle discharge backpressure.

Note: Nozzle coefficient (efficiency) is determined based upon proven tested nozzle configuration flow testing.