Flow Rate & Velocity: Solution Found

[grscott_2000]

Question solved

 

[HallsofIvy]

The problem..
I have been given a flow rate in units of m^3 per second. I also know the diameter of the pipe the fluid is flowing in meters.

I have to calculate the velocity of the flow and give the answer in units of ms^-1


Relevant values..
pipe diameter = 0.6m
flow rate = 5 m^3 per second


My answer...

I know that

flow rate = cross sectional area x velocity

So all things considered I should just be able to rearrange the equation to give

velocity = flow rate / area = 5 / (pi * .15 * .15) = 70.7 ms-1

No, if the diameter of the pipe is .6 m then its radius is .6/2= .3 m.

You should have 5/(pi* .3* .3)= 17.7 m/s.

Second point...

I also know that

velocity = 4 * flow rate / (pi * (pipe diameter)^2)

Yes, this is exactly the same thing: diameter= 2*radius so (diameter)^2= 4*radius. Canceling the "4" in the numerator and denominator gives exactly what you have above.

Which gives a completely different answer...

(4 * 5) / ((pi * 0.6)^2) = 17.68 ms-1

Although you have the correct answer, there is a typo on the left: "pi" should not be squared.

I would very much appreciate anyone who can help me out with this apparent annomily. I tend to think that the second point is correct because I can plug various values into it, rearrange etc and still get a sensible answer