Finding the area of a pipe, rate of flow

[bnosam]

Homework Statement

Water flows from a pipe at 650 L/min. a) What is the diameter of the pipe (in cm) of that pipe, if the water flows at 1.5 m/s?

Homework Equations

Q = V*A

Now the equation for the area of a pipe is A = ∏r^2

The Attempt at a Solution

Q = 650 L/min
V = 1.5 m/s

So the equation should be A = Q/V

A = (650 L/min) / (1.5 m/s)

Now after this part I really have no clue, my next guess would be to possibly change units? But I'm not quite sure which units I'd have to change to to get the answer.

I looked in the back of my book and the answer is 9.6 cm, but what use is the answer if you can't get there, right?

Any help, hints etc would be appreciated :) thanks

 

[Simon Bridge]

How many liters are there in a cubic meter?
Hint 1 litre = 1 cubic decimeter = a cube 10cm on each side.

 

[bnosam]

How many liters are there in a cubic meter?
Hint 1 litre = 1 cubic decimeter = a cube 10cm on each side.

A cubic metre would contain 1000 litres.

I just solved it...turns out I was putting the decimal point in the wrong place...oh my gosh. Hahaha

Thanks Simon.

 

[Simon Bridge]

No worries. Just got to watch those conversion factors ;)
Simon

 

[Nickie]

I would approach this problem by first converting all units to a common system. In this case, since the given rate of flow is in L/min and the given velocity is in m/s, I would convert the rate of flow to m^3/s. This can be done by multiplying 650 L/min by (1 m^3 / 1000 L) and dividing by 60 s/min.

650 L/min * (1 m^3 / 1000 L) * (1 min / 60 s) = 0.01083 m^3/s

Now that we have all units in the same system, we can use the equation A = Q/V to solve for the area of the pipe. However, we need to rearrange the equation to solve for the radius first.

A = ∏r^2
r^2 = A/∏
r = √(A/∏)

Now, we can plug in the values we know into the equation.

r = √(0.01083 m^3/s / ∏)
r = 0.0586 m

Finally, we can convert the radius to cm, as requested in the problem.

r = 0.0586 m * (100 cm / 1 m) = 5.86 cm

Therefore, the diameter of the pipe is twice the radius, or 2*5.86 cm = 11.72 cm. This is close to the given answer of 9.6 cm, so it is possible that the answer in the back of the book is incorrect.