You are asked to estimate the water flow rate in a pipe of radius 3 meters at a

Question

You are asked to estimate the water flow rate in a pipe of radius 3 meters at a remote area location with a harsh environment. The flow rate Q is given by You already know that velocity varies along the radial location, but you do not know how it varies. To save money, you are allowed to put only two velocity probes (these probes send the data to the central office in New York, NY via satellite) in the pipe. Radial location, r is measured from the center of the pipe. That is to say, r = 0 is the center of the pipe and r = 3 meters is the wall of the pipe. One radial location for the velocity probe is given by 3/2 + 3/2 (1/N3). The radial location you would suggest for the other velocity probe in order to obtain the most accurate calculation of the flow rate is (enter your answer as a decimal number and keep 4 decimal places)

Explanation / Answer

V = VMAX [1 - (r/R)]n WHERE n is a arbitary number. R= 3 m

One detector is place at 3/2 +3/2*(1/sqrt3) = 2.366 m.

So, r/R = 2.366/3 = 0.788. So another must be place at a distance so that r/R=0.212 condition follows. [1-0.788 =0.212]

that means r= R*0.212 = 3*0.212 = 0.636 m distance from the centre.

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