Answer to Question #107186 in Physical Chemistry for Bharti

Question #107186
Water flows through an 8-in steel pipe at an average velocity of 6ft/s. Downstream the pipe devides into 8inch main and 2-in-bypass. The equivalent length of the bypass is 22ft; the length of the 8in pipe in the bypassed section is 16ft. Neglecting entrance exit losses what fraction of the total water flow passes through the bypass? ( Fluid mechanics)
1
Expert's answer
2020-03-31T12:41:13-0400

Volume flowrate (volume of water per second) is constant before pipe branching and in the by-passed section. It equals to pipe section ("\\pi"r2) multiplied by velocity (v):

vmain*"\\pi"*rmain2 + vbypass*"\\pi"*rbypass2 = 6*"\\pi"*(8/2)2 = "\\pi"*6*16 in2*ft/s

For the steady water flow, time to come through 22 ft bypass should be equal to time of water passing through the 16 ft bypassed mainline. It means that: 22/vbypass = 16/vmain.

Solving both equations, we find that vbypass = 8.6 ft/s and vmain = 5.5 ft/s.

Fraction of water passed through bypass is then "\\pi"*rbypass2*vbypass devided by total volume flowrate:

8.6*"\\pi"*(2/2)2/(6*"\\pi"*16) = 8.6/(6*16) = 0.0896

i.e. fraction through bypass is 8.96 %



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