How to calculate rate of tank pressure change

[Alfredo78]

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:

Homework Statement

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?

Homework Equations

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

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

Al

 

[LowlyPion]

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:

Homework Statement

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?

Homework Equations

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

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.

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.

 

[Alfredo78]

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

then...

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

I feel like I'm missing something

 

[LowlyPion]

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

then...

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

I feel like I'm missing something

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:

The mean molar mass of air is 28.97 g/mol.

http://en.wikipedia.org/wiki/Earth's_atmosphere

Of course that's grams per Mole, but you can convert.

 

[LowlyPion]

Also at the same link I see:

R = 53.34 ft·lbf·°R−1·lbm−1 (for air)

 

[Alfredo78]

Also at the same link I see:

Thanks for the help! I finally figured it out. The answer is 28.24 lb/ft^2/sec!

 

[LowlyPion]

Thanks for the help! I finally figured it out. The answer is 28.24 lb/ft^2/sec!

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

Hopefully, so will your grader.

Cheers.