Fluid Mechanics: Flow rate required to achieve a constant height

In summary, the volume flow rate (Q) in, must equal the volume flow rate out. If that's the case, then the flow rate in is equal to the flow rate out.
  • #1
WhiteWolf98
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Homework Statement
A surface water drain causes your basement to flood at the steady rate of ##2.5~cm/hour##. The basement floor area is ##121~m^2##. At what flow rate (in ##m^3/s## should a pump operate to keep the water accumulated in your basement at a constant level? (give your answer in ##m^3/hour##).
Relevant Equations
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Some thoughts that I've had on the question are saying the volume flow rate (##Q##) in, must equal the volume flow rate out. If that's the case, then:

##Q_{in} = Q_{out}##

##A_1V_1=A_2V_2##

But... no areas have been given. And height doesn't enter this equation at all.

Then I thought it could have something to do with Torricelli's Law.
##\Delta t = \frac {2A} {a \sqrt {2g}} (\sqrt {h_1} - \sqrt {h_2} ##

But again, still, no areas are given. Also, if the height is constant, then:

##\sqrt {h_1} - \sqrt {h_2} = 0##

So the whole equation becomes zero. Besides of which, velocity isn't in that equation at all.

Finally, I thought Bernoulli; that's just out of the question though. There's no streamline.

I know I need to link the height with velocity and somehow area, but I can't find a relationship.
 
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  • #2
WhiteWolf98 said:
the volume flow rate (Q) in, must equal the volume flow rate out
Right, so what is the flow rate in in this case?
 
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  • #3
Do you mean the flow rate of the water into the basement? How can I calculate the flow rate in without knowing the area of the water drain?

I do know the area of the basement however... So, first I converted the speed of the water from ##\frac {cm} {hour}## to ##\frac m s##. I then multiplied this speed by the area of the basement to obtain a flow rate. Which, I guess is still the flow rate in...?
 
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  • #4
WhiteWolf98 said:
Which, I guess is still the flow rate in...?
Yes.
WhiteWolf98 said:
the speed of the water
To be clear, it is the rate of rise of the water if nothing is flowing out.
 
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  • #5
Oh. So I've pretty much solved the question... There's not really anything more to do. The flow rate out has to be equal to what I've calculated.

Guess the answer was simpler than I thought. Thank you
 

Related to Fluid Mechanics: Flow rate required to achieve a constant height

1. What is fluid mechanics?

Fluid mechanics is a branch of physics that deals with the study of fluids and their properties, including how they flow and interact with their surroundings.

2. How is flow rate measured?

Flow rate is typically measured in volume per unit time, such as liters per second or cubic meters per hour. It can be measured using instruments such as flow meters or by calculating the change in volume over a specific time period.

3. What factors affect the flow rate of a fluid?

The flow rate of a fluid can be affected by several factors, including the viscosity of the fluid, the pressure difference between two points, the size and shape of the container or pipe, and the presence of any obstacles or restrictions in the flow path.

4. How can the flow rate be increased to achieve a constant height?

In order to achieve a constant height, the flow rate must be controlled and maintained at a specific value. This can be achieved by adjusting the pressure difference, changing the size or shape of the container or pipe, or using pumps or valves to regulate the flow rate.

5. What are some real-world applications of fluid mechanics?

Fluid mechanics has many practical applications in various fields, such as engineering, medicine, and environmental science. Some examples include designing efficient water and sewage systems, creating aircraft and automobile designs, and studying blood flow in the human body.

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