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Homework Help: How to calculate rate of tank pressure change

  1. Aug 14, 2008 #1
    Hello everyone,
    I'm new to the forum and after doing a basic search I wasn't able to find anything that would help me with a particular problem. I'm taking an online Aerodynamics course with Embry-Riddle and I can't figure out how to solve the following:

    1. The problem statement, all variables and given/known data

    If air is being pumped into a 10 ft^3 tank at a rate of 0.01 lbm/sec, and the tank temperature is being held constant at 70 F. How fast (lb/ft^2/sec) is the pressure in the tank rising?

    2. Relevant equations

    Equation of state (pressure = density*specific gas constant*temperature)
    dp/dt=dM/dt * RT/V (or something like that)

    3. The attempt at a solution

    I tried to get things going by solving for pressure with standard sea-level density then finding the mass (mass= density*volume) but.....then I just get lost.

    Any help would be greatly appreciated. Thanks

  2. jcsd
  3. Aug 14, 2008 #2


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    It looks like you are on the right track.

    PV = NRT

    V and T are being held constant. R is a constant so all you need to translate is the rate that Pressure changes (dP/dt time not temp) consistent with the change in lbs of air / sec. You need to relate the given change in lbs of air to the change in N which is the number of moles of air to satisfy the ideal Gas Law.

    This yields your dP/dt = dN/dt * RT/V

    Make sure your units are correct.
  4. Aug 14, 2008 #3
    So....If 0.01 is my mass rate of change....

    P=NRT= (2.3769*10^-3)(1716)(530)=2161.74

    and Mass= density*volume = 2.3769*10^-2 slugs * 10ft^3

    multiplied by weight of air, 32.2=.765 lbm

    then multiplied by mass rate of change .01 lbm/sec = .00765 lbm/sec


    dp/dt=dN/dt*RT/V = 0.00765 * (1716)(530)/10= 695.75?

    I feel like I'm missing something:confused:
  5. Aug 14, 2008 #4


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    Careful. I don't think density is quite the right approach. I'd suggest focusing on the rate of change of mass. What you are looking for is Moles to satisfy the Perfect Gas Law equation. What you are given is mass as a rate of change. Convert mass to moles. I believe that it is the rate of change of moles that gives you your rate of change of Pressure scaled by the effect of the other constants in the relation.

    Perhaps this helps:

    Of course that's grams per Mole, but you can convert.
    Last edited: Aug 14, 2008
  6. Aug 15, 2008 #5


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    Also at the same link I see:

  7. Aug 16, 2008 #6
    Thanks for the help! I finally figured it out. The answer is 28.24 lb/ft^2/sec!
  8. Aug 16, 2008 #7


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    I didn't calculate anything. I will defer to your arithmetic.

    Hopefully, so will your grader.

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