# Equation relating mass flow rate to pressure drop

1. Aug 12, 2009

### jill p

Hi
I am designing a heat exchanger. I know the mass flow rate required for cooling. I have calculated the pressure drop for current design. How do I work out if the size if the heat exchanger can handle the flow rate ? Does the mass flow rate depend on the size of the heat exchanger tubes ? Is there an equation relating mass flow rate to pressure drop ?

Thank you very much

2. Aug 12, 2009

### minger

You've somehow worked out the pressure drop without calculating the flow rate? Would you care to clarify? Was there just some imperical formula you used?

If you're referring to losses through the tubes, then you can just use Darcy-Weisbach for straight tubes with bends. If you want the pressure loss through the shell, there are imperical relations for cross-flow through tubes.

3. Aug 13, 2009

### jill p

hi minger

thnx. calculated flow rate using q=mc(t2-t1). then calc pressure drop. is flowrate dependent on hxr tube size ?

thx

4. Aug 13, 2009

### jaap de vries

Ok so you calculated the required flow rate first, thats OK.

Tube size mater a lot, small narrow tubes = large head loss. First define you system. How low, narrow, how many bends, are there baffles? then calculate required Reynolds number (Note that temperature change and so does change the viscosity (of water). You can probably take the properties at an average temperature. Then, use the equations proposed by minger above.

good luck

5. Aug 13, 2009

### minger

$$Q = mC\Delta T$$ is the equation for heat required for a temperature change (or vice versa). You really should have checked your units.

Finding the flow is an iterative process as the losses are dependent on it. You can typically start with an inlet and outlet pressure, or velocity. From there you can get a baseline solve and from there calculate losses. Plug those back into the equations and resolve. Rinse and repeat.

6. May 25, 2011

### STANSFIELD

The flow rate I calculated was for determining the bore of a restriction orifice. Using the continuity equation and setting the fluid velocity in a 2" line to a reasonable value (5500 ft / min for gas) I can get a flow rate for use in calculating a restriction bore size. However that does not directly relate to the pressure reduction of the system. If I could calculate a time using the loss of mass through the plate I can determine if the flow I calculated is to great for, or acceptable to limit the pressure loss in the system to 600 PSI / MIN. The flow through the restriction will be sonic at first but will slow once the pressure drops below about 1/2 of the upstream pressure.So there must be a relationship between the flow rate and mass loss, and the pressure reduction in the enclosed system. What that relationship is, is what I need to know.

7. May 25, 2011

### STANSFIELD

Sorry Gentlemen. I thought the mass flow to pressure drop title was my problem. I realize now that the replys were related to a heat exchanger question. I am new to this site and I am still learing the ropes.

8. Jun 27, 2011

### W R-P

Hi I'm new here and I just came across this topic.
Well you can take your inlet as point 1 and outlet as point 2, then apply bernoulli's equation.

[(p1/w) + (v1^2/2g) + (z1)] = [(p2/w)+ (v2^2/2g) + (z2) + losses]
where the symbols have their usual meaning
z- elevation from datum
w- specific weight of fluid
the losses are given by (4fl(v^2)/2gd)
where v- pipe velocity
f- Darcy coefficient

If you have a design flow rate, Q (m3/s), you can find the pipe flow velocity V, by dividing Q by the pipe cross section. For this value of V, find the reynold's number (density x pipe velocity x pipe diameter/dynamic viscosity of fluid).find the Darcy coefficient using a moodychart, http://en.wikipedia.org/wiki/Moody_chart. Then find the losses.

If you know the flow rate, pipe length and diameter, you can find the pressure change across the exchanger.
If you know the pressure change, flow, and pipe diameter, you can find the pipe length.

These are just a few of the ways to approach this problem.FEEL FREE TO CORRECT ME.

Last edited: Jun 27, 2011
9. Apr 22, 2013

### ganesanrs

Hi.. Stable air pressure of a chamber is 10PSIG. If the leak rate is 5cc/min, what will be pressure loss / minute inside the chamber?