Equation relating mass flow rate to pressure drop

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Discussion Overview

The discussion revolves around the relationship between mass flow rate and pressure drop in the context of designing a heat exchanger. Participants explore how tube size affects flow rate and pressure loss, and they seek equations or methods to quantify these relationships.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant questions how pressure drop was calculated without first determining flow rate, suggesting the use of empirical formulas for losses through tubes.
  • Another participant confirms that tube size significantly impacts head loss, emphasizing the need to define the system's characteristics before calculations.
  • There is mention of using the continuity equation to determine flow rates for specific applications, such as calculating restriction orifice sizes.
  • A participant introduces Bernoulli's equation as a method to analyze pressure changes and losses in the system, detailing the variables involved.
  • Concerns are raised about the iterative nature of finding flow rates due to their dependence on pressure losses.
  • One participant expresses confusion about the topic's focus, indicating a learning curve in navigating the forum.
  • A later post introduces a separate question about pressure loss in a chamber due to a leak rate, which may not directly relate to the main discussion.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the specific relationship between mass flow rate and pressure drop, as multiple approaches and equations are suggested, and some participants express uncertainty about their calculations and methods.

Contextual Notes

Participants mention various assumptions, such as the need for average temperature properties and the iterative process of calculating flow rates and pressure losses. The discussion also highlights the dependence on system definitions, such as tube dimensions and fluid properties.

Who May Find This Useful

Individuals involved in heat exchanger design, fluid dynamics, or related engineering fields may find the discussion relevant, particularly those seeking to understand the interplay between flow rates and pressure drops in thermal systems.

jill p
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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
 
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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.
 
hi minger

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

thx
 
Ok so you calculated the required flow rate first, that's 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
 
You confused your variables.
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.
 
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.
 
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.
 
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:
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?
 

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