How Do You Calculate the Radius of a Pipe in Fluid Mechanics?

AI Thread Summary
To calculate the radius of a pipe in fluid mechanics, the volume flow rate equation Q = πR^4(P1-P2) / 8nL is used, where Q is the flow rate, R is the radius, P1 and P2 are pressures, n is the fluid's viscosity, and L is the length of the pipe. The user initially struggled with the calculation, questioning whether the differential pressure should be interpreted as a height difference or actual pressure. After clarification, it was confirmed that the height difference of 0.045 m can be used to find the pressure difference using the formula ΔP = ρgΔh. The user successfully recalculated the radius after this understanding. The discussion highlights the importance of correctly interpreting variables in fluid mechanics equations.
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Homework Statement


Water (n = 1.00 10-3 Pa·s) is flowing through a horizontal pipe with a volume flow rate of 0.029 m3/s. As the drawing shows, there are two vertical tubes that project from the pipe. From the data in the drawing, find the radius of the horizontal pipe.

11_80.gif


Homework Equations



Q = πR^4(P1-P2) / 8nL


The Attempt at a Solution



0.029 = πR^4(0.045) / (8*10^-3 * .7)

solve for R, multiply by 100. However, i don't get the right answer...


What am i doing wrong? this seems like such a straightforward problem
 

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Is the differential pressure, (P1 - P2), in the formula given as the head (height or depth) of water (0.045 m), or is it pressure, in which case \DeltaP = \rhog\Deltah, where \Deltah is the difference in heights of the water columns, i.e. 0.045 m.
 
oh maybe it's pgh. let me give it a second go.
 
yes i got it right. thank you Astronuc for the fast reply! I owe you :)
 

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