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

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In summary, the problem involves water flowing into a cylindrical tank through two pipes and leaving through a circular outlet pipe. In order for the water level to remain constant, the mass flow rates of the incoming and outgoing water must be equal. Using the continuity of mass equation, the average flow velocity in the outlet pipe can be calculated by dividing the mass flow rate by the density and area of the outlet pipe, which gives a final answer of 0.509 m/s.
  • #1
Patdon10
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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?
 
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  • #2
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!
 
  • #3
Are you saying the mass flow rate out has to be equal to 16 kg/sec?
 
  • #4
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.
 
  • #5
right. So I have 16 kg/s in the outlet pipe, but how do I find the velocity from that?
 
  • #6
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?
 
  • #7
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
 
  • #8
technician said:
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.
 
  • #9
mmmmm. I think it is OK 20cm is a large pipe:biggrin:
 
  • #10
That looks like the correct answer
 
  • #11
Thanks for the help. I'll run with it.
 

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

1. What is incompressible flow?

Incompressible flow is a type of fluid flow where the density of the fluid remains constant, regardless of changes in pressure or velocity. This means that the volume of the fluid does not change as it moves through a system.

2. How is incompressible flow different from compressible flow?

Incompressible flow is characterized by a constant density, while compressible flow is characterized by a varying density. Compressible flow is typically seen in high-speed, high-pressure systems, while incompressible flow is seen in low-speed, low-pressure systems.

3. What are some examples of incompressible flow?

Incompressible flow can be seen in many everyday situations, such as the flow of water through pipes, the flow of blood in our bodies, and the flow of air around a moving car. It is also commonly seen in hydraulic systems, pumps, and turbines.

4. What are the applications of studying incompressible flow?

Understanding incompressible flow is crucial in many engineering and scientific fields, such as aerodynamics, hydrodynamics, and fluid mechanics. It is also used in the design and analysis of various systems, such as aircraft, ships, and pipelines.

5. How do scientists and engineers analyze incompressible flow?

Scientists and engineers use various mathematical models and equations, such as the Navier-Stokes equations, to analyze incompressible flow. They also use computational fluid dynamics (CFD) simulations and experiments to study and predict the behavior of incompressible fluids in different systems.

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