Physics, 15.04.2021 15:30 eemorales5100

A 3-m-diameter tank is initially filled with water 2 m above the center of a sharp-edged 10-cm-diameter orifice. The tank water surface is open to the atmosphere, and the orifice drains to the atmosphere through a 100-m-long pipe. The friction coefficient of the pipe is taken to be 0.015 and the effect of the kinetic energy correction factor can be neglected. Determine (a) the initial velocity from the tank (5 points); and (b) the time required to empty the tank (5 points). (Q.8-78, E-book)

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Answer from: carliehanson9908

a) 1.542 m/s

b) t = 38.91 mins

Explanation:

Given data:

Diameter of tank ( D ) = 3 m

height of tank ( initial ) ( h = z1 ) = 2m

Diameter of sharp edged orifice = 0.1 m

pipe length ( L ) = 100 m

coefficient of friction of pipe ( f ) = 0.015

∝1 = ∝2 = 1

A) calculate initial velocity from the tank

since the fluid is open to the atmosphere ; p1 = p2 = Patm ( atm pressure )

the initial velocity of the tank can be determined with the equation below

V = $\sqrt{\frac{2gZ1}{1 + f \frac{L}{d} + K _{L} } }$ ---- ( 1 )

where : Z1 = 2m , f = 0.015, L = 100m , Kl = 0.5m , d = 0.1 m , g = 9.81m/s^2

input given values into equation 1 above

V = 1.542 m/s

b) Determine time required to empty tank

Given velocity = $\sqrt{\frac{2gZ1}{1 + f \frac{L}{d} + K _{L} } }$ and Flow rate = $\sqrt{\frac{2gZ1}{1 + f \frac{L}{d} + K _{L} } }* \frac{\pi }{4} *d^2$

differentiate the flow rate ( dt ) and then integrate the equation to get the required expression

t = $\frac{2D^2}{d^2} \sqrt{\frac{(1+f\frac{L}{d}+K_{L})Z_{1} }{2g} }$ -------- ( 2 )

where : : Z1 = 2m , f = 0.015, L = 100m , Kl = 0.5m , d = 0.1 m , g = 9.81m/s^2, D = 3m

input values into equation 2

t = 38.91 mins

Answer from: Quest

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Answer from: Quest

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