Bernoulli's Principle

Problem # 1:

Water at a gauge pressure of 3.8 atm at street level flows in to an office building at a speed of 0.06 m/s through a pipe 5.0 cm in diameter. The pipes taper down to 2.6cm in diameter by the top floor, 20 m above. Calculate the flow velocity and the gauge pressure in such a pipe on the top floor. Assume no branch pipe and ignore viscosity.


Solution:

By continuity equation:

v2 = (A1v1) / A2 = (π (5.0 / 2)2 (0.60) ) / ( π (2.6 / 2)2) 

v2 = 2.2 m/s

By Bernoulli’s Equation:

P1 + ρgh1 + ½ρ(v1)2 = P2 + ρgh2 + ½ρ(v2)2              (Po = atmospheric pressure)

P2 = (3.8 x Po) + Po + ½(1000)(0.6)2 – (1000)(9.8)(20) – (1000)½(2.2)2

P2 = 2.8 x 105 Pa