Solve Drying Room Issue: Calculate Air Flow Speed & Mass Flow Rate

[Dr_awkward]

Hello everyone!

Here is the problem:
The air removal in a drying room is done via a pipe (length 6 m, diameter 100 mm and surface roughness 0,152mm). The pipe system is composed of a sharp edged entrance and 4 standard 90 degrees turns. The excess pressure in the dryer is 50 Pa. Calculate the flow speed at which the air is removed from the dryer as well as the mass flow rate.
The temperature of the air is 37 celsius degrees (density: 1,12kg/m³ dynamic viscosity: 1,9.10^-5 kg/ms)
The height drop is negligeable and we assume that the dryer is so big that the flow speed in it is 0 m/s

How far I've gotten:
I thought of using Bernoulli's equation to figure out the speed of the flow, but I think I'm missing some information:

p1-p2=(1/2)*rho*(C2²-C1²)

problem is that I have no idea what is c1 or c2 (speeds) is c1 supposed to be the speed of the flow in the dryer (0 m/s)?

That's where I went first. Then I asked myself what if I had to use the pressure drop equation

delta(p)=(1/2)*rho*C²*(f*(L/d)+sum(K))

The K's (rughness elements) are easy to solve (0,5 for the sharp edge and 0,3 for each of the standard turns) but to solve the friction factor, I need to use the moody chart...but to use it, I need the flow speed for the Reynold's number. So back to square one.

That is pretty much how far I've got and I see no solution in sight. I'm pretty sure it can't be too complicated of an answer.

Thanks ahead for your help, this problem has been bugging me for a while now.

P.S. : excuse my poor English as it is not my native tongue.

 

[SteamKing]

Hello everyone!

Here is the problem:
The air removal in a drying room is done via a pipe (length 6 m, diameter 100 mm and surface roughness 0,152mm). The pipe system is composed of a sharp edged entrance and 4 standard 90 degrees turns. The excess pressure in the dryer is 50 Pa. Calculate the flow speed at which the air is removed from the dryer as well as the mass flow rate.
The temperature of the air is 37 celsius degrees (density: 1,12kg/m³ dynamic viscosity: 1,9.10^-5 kg/ms)
The height drop is negligeable and we assume that the dryer is so big that the flow speed in it is 0 m/s

How far I've gotten:
I thought of using Bernoulli's equation to figure out the speed of the flow, but I think I'm missing some information:

p1-p2=(1/2)*rho*(C2²-C1²)

problem is that I have no idea what is c1 or c2 (speeds) is c1 supposed to be the speed of the flow in the dryer (0 m/s)?

That's where I went first. Then I asked myself what if I had to use the pressure drop equation

delta(p)=(1/2)*rho*C²*(f*(L/d)+sum(K))

The K's (rughness elements) are easy to solve (0,5 for the sharp edge and 0,3 for each of the standard turns) but to solve the friction factor, I need to use the moody chart...but to use it, I need the flow speed for the Reynold's number. So back to square one.

That is pretty much how far I've got and I see no solution in sight. I'm pretty sure it can't be too complicated of an answer.

Thanks ahead for your help, this problem has been bugging me for a while now.

P.S. : excuse my poor English as it is not my native tongue.

The Bernoulli equation by itself is not sufficient to solve this problem. You have fluid flow in a duct with friction.

As a first trial solution, assume fully turbulent flow and find 'f' based on the pipe size. You know the total pressure drop in the system because the pressure in the dryer is 50 Pa above ambient. The only remaining unknown is the velocity in the pipe which equates to a pressure drop of 50 Pa.

You can use the Darcy equation

http://en.wikipedia.org/wiki/Darcy–Weisbach_equation

to relate total pressure drop to the velocity of the air in the pipe. Use this velocity to calculate the Reynolds number of the flow to make sure you are in the fully turbulent region. If you are in the fully turbulent region, the friction factor f will be constant for all Re as long as the pipe diameter and roughness remain constant, and your problem is solved.

I don't expect the velocity of air in the pipe to be high enough that compressibility effects will affect the solution.

 

[Dr_awkward]

Thank you a lot for your help!

I did as you said and assumed that the flow was fully turbulent. From the Moody chart I obtained the friction factor. (f=0,0225)

I then used the Darcy equation in a modified form that adds loss coefficients for pipe components (was given in my syllabus and it's the second one in my first post ) and found a speed of 5,41m/s for a head loss of 50 Pa.
I then checked if the flow was indeed fully turbulent and obtained Re=31890 so everything fine here.

and then I just plugged the data into the mass flow rate equation and got q_m=0,047 kg/s

Thanks again for the help

 

[SteamKing]

I'm glad I could help, and that things worked out for you.