Finding the Average Flow Velocity in a Tank with Multiple Inlets and One Outlet

[Patdon10]

Homework Statement

Water (of density 1000 kg/m^3) flows into a cylindrical tank through two pipes at mass flow rates of 6 kg/sec and 10 kg/sec respectively, and leaves the tank via a circular outlet pipe of 20 cm diameter. If the water level in the tank is to remain constant, calculate the average flow velocity in the outlet pipe.

Homework Equations

Q1 + Q2 = Q3 ---> A1*u1 + A2*u2 = A3*u3

The Attempt at a Solution

I'm really tempted to just say, well the water coming in is 10 kg/sec and 6 kg/sec so the water exiting must be 16 kg/sec. I'm not sure you can do that though, but there are too many unknowns! You have A3, but not A1 or A2. You have u1 and u2, but not u3 (what you're solving for).

A1(6 kg/sec) + A2 (10 kg/sec) = pi*0.2m^2*u3

Can anyone steer me in the right direction?

 

[RTW69]

You are correct, the mass flow rate coming in equals mass flow rate going out via continuity of mass equations. Remember mass flow rate = density*area*velocity. You know the mass flow rate out, area and density. Bingo!

 

[Patdon10]

Are you saying the mass flow rate out has to be equal to 16 kg/sec?

 

[RTW69]

Yes, if the level of the water is not going up the mass of water going in must equal the mass of water going out so 16 kg/s is leaving the outlet pipe.

 

[Patdon10]

right. So I have 16 kg/s in the outlet pipe, but how do I find the velocity from that?

 

[Patdon10]

I got an answer, but it seems rather low. I think I saw somewhere that Velocity = flowrate/area*density

so I have 16/(pi*0.04 m^2)*(1000)
The units work out to be m/s and I got 0.127 m/s That's some slow moving water! Does this work?

 

[technician]

I think you have got the diameter and area of the outlet mixed up... it is 0.2m diameter so the area is π x 0.1^2

 

[Patdon10]

I think you have got the diameter and area of the outlet mixed up... it is 0.2m diameter so the area is π x 0.1^2

Thanks. You're right. That changes the answer to 0.509 m/s
Still seems a little low though.

 

[technician]

mmmmm. I think it is OK 20cm is a large pipe

 

[RTW69]

That looks like the correct answer

 

[Patdon10]

Thanks for the help. I'll run with it.