Water is flowing in a pipe with a varying cross-sectional area, and at all points the water completely fills the pipe. at point 1 the cross-sectional area of the pipe is 0.070m2, and the magnitude of the fluid velocity is 3.50m/s.
part a
what is the fluid speed at point in the pipe where the cross-sectional area is 0.105m2?
part b
what is the fluid speed at point in the pipe where the cross-sectional area is 0.047m2?
part c
calculate the volume of water discharged from the open end of the pipe in 1.00hour.

a) 2.33 m/s

b) 5.21 m/s

c) 882 m³

Explanation:

Using the concept of continuity equation

for flow through pipes

Where,

A = Area of cross-section

V = Velocity of fluid at the particular cross-section

given:

a)

substituting the values in the continuity equation, we get

or

or

b)

substituting the values in the continuity equation, we get

or

or

c) we have,

Discharge

thus from the given value, we get

Also,

Discharge

given time = 1 hour = 1 ×3600 seconds

substituting the value of discharge and time in the above equation, we get

or

volume of flow =

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