Bernoulli Equation: Water flows from a reservoir down a circular pipe of diamete

Question

Bernoulli Equation: Water flows from a reservoir down a circular pipe of diameter D = 1 cm at the instant shown. The difference in height between the water’s surface in the reservoir and the pipe’s outlet is h = 2 m. Assuming viscosity is negligible, calculate the flow rate Q, in cm3/sec, at which water will exit the pipe at the instant shown.

Hints: Pressures at the surface of the reservoir and at the pipe’s outlet are both equal to atmospheric pressure. The reservoir is very large compared to the pipe, so the velocity with which the reservoir’s free surface decreases in height is much smaller than the fluid velocity exiting at the pipe’s outlet.

Explanation / Answer

from bernoulies theorem

1/2*rho*v^2 = rho*gh

v = sqrt(2gh)

v = sqrt(2*9.8*2) = 6.26 m/sec

volume flow rate = A*v = 3.14*r^2*v = 3.14*0.5^2*626 = 491.41 cm^3/sec

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