Equation relating mass flow rate to pressure drop

In summary, the conversation discusses designing a heat exchanger and determining the mass flow rate required for cooling. The pressure drop for the current design has been calculated, but the question remains of whether the size of the heat exchanger can handle the flow rate and if there is an equation relating mass flow rate to pressure drop. The conversation also includes a discussion on calculating flow rate and pressure loss through tubes, as well as using equations such as Darcy-Weisbach and Bernoulli's to solve for pressure change and flow velocity.
  • #1
jill p
2
0
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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  • #2
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
hi minger

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

thx
 
  • #4
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
 
  • #5
You confused your variables.
[tex]Q = mC\Delta T[/tex] 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
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
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
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.
 
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  • #9
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?
 

What is the equation for relating mass flow rate to pressure drop?

The equation for relating mass flow rate (m) to pressure drop (ΔP) is given by the relationship m = (ΔP * A)/√(ρ * K), where A is the cross-sectional area of the flow, ρ is the density of the fluid, and K is a constant determined by the fluid's properties and the geometry of the system.

How does the cross-sectional area of a flow affect the mass flow rate?

The cross-sectional area of a flow (A) has a direct effect on the mass flow rate, as seen in the equation m = (ΔP * A)/√(ρ * K). A larger cross-sectional area allows for a greater volume of fluid to flow through, resulting in a higher mass flow rate. Similarly, a smaller cross-sectional area will result in a lower mass flow rate.

What role does fluid density play in the equation for mass flow rate and pressure drop?

Fluid density (ρ) is a crucial factor in the equation, as it is directly proportional to the mass flow rate. A higher fluid density will result in a higher mass flow rate for a given pressure drop, while a lower fluid density will result in a lower mass flow rate.

How does the constant K impact the equation for mass flow rate and pressure drop?

The constant K takes into account the fluid's properties and the geometry of the system, and therefore it can vary depending on the specific situation. It is typically determined experimentally or through theoretical calculations. A higher value of K will result in a lower mass flow rate for a given pressure drop, and vice versa.

What are some real-life applications of the equation relating mass flow rate to pressure drop?

This equation is commonly used in industries such as chemical and petroleum engineering, where it is important to understand the relationship between pressure drop and mass flow rate in order to optimize process efficiency. It is also used in HVAC systems to determine the flow rate of air or other fluids through ducts and pipes, and in medical devices such as respirators to monitor and control the flow of gases.

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