A liquid of density 1288 kg/m3 flows with speed 2.88m/s into a pipe of diameter

Question

A liquid of density 1288 kg/m3 flows with speed 2.88m/s into a pipe of diameter 0.24 m. The diameter of the pipe decreases to 0.05 m at its exit end. The exit end of the pipe is 3.34 m lower than the entrance of the pipe, and the pressure at the exit of the pipe is 1.4 atm.

a) What is the velocity v2 of the liquid flowing out of the exit end of the pipe? Assume the viscosity of the fluid is negligible and the fluid is incompressible. The acceleration of gravity is 9.8 m/s2 and Patm = 1.013 105 Pa.

Answer in units of m/s

b) Applying Bernoullis principle, what is the pressure P1 at the entrance end of the pipe?

Answer in units of Pa

Explanation / Answer

radius at the initial end = 0.24/2 = 0.12m
radius at the end = 0.05/2 = 0.025m
using equation of continuity
A1V1 = A2V2
=> (0.12)2 * 2.88 = (0.025)2 * V2
=> V2 = 66.35 m/s

(a) so velocity at the exit end = 66.35 m/s


(b) using bernaulli's theorem
P1 + gh1 + (1/2) v12 = P2 + gh2 + (1/2) v22
P1 + 0 + 1854.72 = 1.4 * 1.013 * 105 + 42158.816 + 2835095.69
P1 = 141855 + 42158.816 + 2835095.69 - 1854.72
    = 3017254.786 Pa
    = 30.17 atm

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

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