The concepts that play roles in this problem are similar to those in Multiple-Co

Question

The concepts that play roles in this problem are similar to those in Multiple-Concept Example 15, except the fluid here moves upward rather than remaining horizontal. A liquid is flowing through a horizontal pipe whose radius is 0.0290 m. The pipe bends straight upward through a height of 5.30 m and joins another horizontal pipe whose radius is 0.0772 m. What volume flow rate will keep the pressures in the two horizontal pipes the same?

The concepts that play roles in this problem are similar to those in Multiple-Concept Example 15, except the fluid here moves upward rather than remaining horizontal. A liquid is flowing through a horizontal pipe whose radius is 0.0290 m. The pipe bends straight upward through a height of 5.30 m and joins another horizontal pipe whose radius is 0.0772 m. What volume flow rate will keep the pressures in the two horizontal pipes the same?

Explanation / Answer

P1 + 1/2 rho v1^2 = P2 + 1/2 rho v2^2 + rho g h

flow rate = Av1 = Av2

v1 = f/pi*0.029^2 and v2 = f/pi*0.0772^2

so

1/2*( f/(pi*0.029^2))^2 = 1/2*( f/(pi*0.0772^2))^2 + 9.81*5.3

flow rate=0.0272

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