## Process flow diagram: pressure and velocity changes with temperature

Hello everyone,

I have a process in which a gas goes through a heater. I want to calculate the physical properties of the stream coming out of the heater. Here is a description of the streams:

Input to the heater:
molar flow rate is 1 mole per minute
pressure(P) is 2 atm
temperature(T) is 298K
gas velocity(u) is 1 cm per second

Output from the heater:
molar flow rate is 1 mole per minute
pressure is unknown
temperature is 1073K
gas velocity is unknown

How do I go about solving for the pressure and velocity of the output, assuming that the gas is compressible (i.e. - the density is free to change)?

Assuming an ideal gas equation of state: P = rho*R*T/M where rho = density, R = gas constant, and M = molar mass of the gas species.

Continuity (molar flux in equals molar flux out) requires that the molar flow rates be equal, but not necessarily the volumetric flow rates since density is free to change.

I end up getting stuck at the equation when combining ideal gas and continuity expressions:
P1*u1*T2/T1 = P2*u2

I cannot figure out how P2 and u2 individually change.

Help?

Thanks!
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 Blog Entries: 7 Recognitions: Gold Member Homework Help Science Advisor Hi uby. The way to do this is to go back to basic principals and perform an analysis on the heat transfer and pressure drop through the heat exchanger. I'd suggest breaking up the flow through the heat exchanger into smaller chunks (ie: control volumes) and performing a pressure drop analysis on each bit of the flow along with a heat transfer analysis to determine how temperature (really the enthalpy) of the flow changes. As heat is added, the fluid properties change, and as fluid properties change, pressure drop along a given length of tube inside the heat exchanger also change.
 Hi Q_Goest, Thanks for your reply! I'm not sure I agree with (or I fail to understand) your suggestion. Isn't the ideal gas equation of state derived from similar principles as the heat transfer equations (i.e. - work and heat in the forms of enthalpy and internal energy)? The ideal gas equation of state states that the increase in temperature should manifest itself as a change in pressure AND/OR velocity/fluid density. I'm not sure I gain any additional information from performing heat transfer calculations. Think of this as a state function: I don't care how or at what rate the fluid temperature increases, all I care about is what happens after it reaches a specified temperature. Shouldn't the equation of state give that to me directly?

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