Answer to Question #107186 in Physical Chemistry for Bharti

Question

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)

Answer 1

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):

v_main*$\pi$*r_main² + v_bypass*$\pi$*r_bypass² = 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/v_bypass = 16/v_main.

Solving both equations, we find that v_bypass = 8.6 ft/s and v_main = 5.5 ft/s.

Fraction of water passed through bypass is then $\pi$*r_bypass²*v_bypass 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 %