Vent line pressure and mass flow rate

[gfd43tg]

Homework Statement

1. An emergency vent line from a reactor is 55 feet long and has an inside diameter of 4.026 inches. The surface roughness of the pipe is 0.0012 inches. The line discharges hydrogen to the atmosphere (P = 14.7 psia)

a) If the mass flow rate of hydrogen is 95 lb / minute and the temperature is 100 F, what is the pressure within the vessel ? Assume the gas flow is isothermal.

b) Could a mass flow rate of 100 lb/minute be attained in this emergency vent line with this vessel pressure ??

Data for hydrogen: μ = 0.014 cP
Cp = 3.5 BTU/lb F
γ = 1.4
Z = 1.00

Homework Equations

The Attempt at a Solution

I solved part (a), I assumed subsonic flow, then used the equation shown in my attempt to basically guess P1 until it equaled G.

For part (b), I'm a little bit hesistant, because I don't know how the pressure at the discharge could be any lower than atmospheric, hence the mass flow rate is already at a maximum. But I'm a bit hesistant because they gave information about the specific heat, and I am unsure what to do with it or γ.

 

[SteamKing]

No, the flow can't exit at below-atmospheric pressure.

It's not clear what you did since you don't show any calculations.

 

[gfd43tg]

Sorry again, I was doing this at close to 3 AM, thought I had everything posted. Here is my attempt

 

[Chestermiller]

Maybe doing it adiabatically so the gas cools as it expands. This would result in lower gas velocities and less of a pressure drop for the same mass flow rate. Another possible factor might be the effect of lower temperature on the viscosity; if I remember correctly, the viscosity of a gas increases with increasing temperature.

Chet

 

[Chestermiller]

Second Thoughts. I've had some second thoughts about my previous response. In the existing setup, if we apply the first law of thermo to the system (continuous flow version), the shaft work is zero, and, if the system were run adiabatically instead of isothermally, the change in enthalpy per unit mass would be zero. If the change in enthalpy is zero, then the temperature change has to be zero (ideal gas). So running the system adiabatically would give the same result, since it is already adiabatic. So maybe the answer should be to cool the gas in the vent line.

Chet

 

[gfd43tg]

Whats the specific heat information given for? Do you think that this is just a conceptual question, or they are looking for a calculation?

 

[SteamKing]

You've assumed that the flow of H2 thru the vent is subsonic. Is that assumption borne out by your calculations? What is the velocity of the flow of H2 in the vent pipe? What's the speed of sound in H2 at 100 F?

 

[Chestermiller]

You've assumed that the flow of H2 thru the vent is subsonic. Is that assumption borne out by your calculations? What is the velocity of the flow of H2 in the vent pipe? What's the speed of sound in H2 at 100 F?

SteamKing is right. That calculated exit velocity looks pretty high if you assume subsonic flow. I calculate about 3700 ft/sec. As he suggested, check out the speed of sound of H2 at 100F. This is one way that the γ comes in. You may have to redo the calculation, dropping the subsonic approximation.

Chet

 

[SteamKing]

SteamKing is right. That calculated exit velocity looks pretty high if you assume subsonic flow. I calculate about 3700 ft/sec. As he suggested, check out the speed of sound of H2 at 100F. This is one way that the γ comes in. You may have to redo the calculation, dropping the subsonic approximation.

Chet

Chet:
Using Maylis' calculations, I figure V to be about 1627 ft/s, given the area of a 4.026" ID pipe, m-dot of 1.583 lbm/s and a density of H2 of 0.011 lbm/ft^3 @ P = 33.4 psia.

 

[Chestermiller]

Chet:
Using Maylis' calculations, I figure V to be about 1627 ft/s, given the area of a 4.026" ID pipe, m-dot of 1.583 lbm/s and a density of H2 of 0.011 lbm/ft^3 @ P = 33.4 psia.

YES. That agrees with my value of 3700 ft/s at the exit pressure of 14.7 psia.

Chet

 

[gfd43tg]

I calculated the sonic velocity to be 3732.6 ft/s, and the velocity of the H2 to be 3660.9 ft/s, so the subsonic velocity assumption is correct. I then calculated G for part (b), and got that the velocity is greater than sonic velocity, thus not possible.

 

[SteamKing]

I calculated the sonic velocity to be 3732.6 ft/s, and the velocity of the H2 to be 3660.9 ft/s, so the subsonic velocity assumption is correct. I then calculated G for part (b), and got that the velocity is greater than sonic velocity, thus not possible.

The assumption of incompressibility is only valid if the Mach number of the flow is less than about 0.3. Your calculations show a Mach No. of about 1.

 

[Chestermiller]

The assumption of incompressibility is only valid if the Mach number of the flow is less than about 0.3. Your calculations show a Mach No. of about 1.

Don't those P²'s in the analysis mean that he had included compressibility?

Chet

 

[SteamKing]

Chet:

I haven't gone thru Maylis' calculations in detail. It's not clear from a casual glance at them what is concluded.

 

[Chestermiller]

Chet:

I haven't gone thru Maylis' calculations in detail. It's not clear from a casual glance at them what is concluded.

His calculations actually did take into account compressibility. He expressed the density (in the pressure gradient equation) in terms of the ideal gas law, and brought the p from the density relation (that was in the denominator) over to the dp/dx side of the equation.

Chet