Water flows through a pipe as shown in the figure. The pressure at points 1 and

Question

Water flows through a pipe as shown in the figure. The pressure at points 1 and 2 respectively is 1.90 x 10^5 Pa and 1.20 x 10^5 Pa. The radius of the pipe at points 1 and 2 respectively is 3.70 cm and 1.50 cm. If the vertical distance between points 1 and 2 is 2.75 m, determine the following.
[There is a pipe that begins at the left with an opening labeled P_1, then bends up and to the right to end at an opening labeled P_2. The center of the pipe at P_2 is a height labeled y higher than the center of the pipe at P_1.]
(a) speed of flow at point 1

(b) speed of flow at point 2

(c) volume flow rate of the fluid through the pipe

Explanation / Answer

by bernoulli's theorem

P1 + 0.5 * d * v1^2 + dgh1 = P2 + 0.5 * d * v2^2 + dgh2

P1 + 0.5 * d * v1^2 = P2 + 0.5 * d * v2^2 +  dg(h2 - h1)

1.9 * 10^5 + 0.5 * 1000 * v1^2 = 1.2 * 10^5 + 0.5 * 1000 * v2^2 + 1000 * 9.8 * 2.75 --------------(1)

by continuity equation

A1 * v1 = A2 * v2

pi * 0.037^2 * v1 = pi * 0.015^2 * v2 -----------------(2)

solving equation 1 and 2 we'll get

speed of flow at point 1 v1 = 1.546 m/s

speed of flow at point 2 v2 = 9.406 m/s

volume flow rate = area * velocity

volume flow rate = pi * 0.037^2 * 1.546

volume flow rate = 0.006649 m^3/s

Related Questions

Navigate

• Browse (All)
• Browse W
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.