Question

# A liquid of density 1.33 × 103 kg/m3 flows steadily through a pipe of varying diameter...

A liquid of density 1.33 × 103 kg/m3 flows steadily through a pipe of varying diameter and height. At location 1 along the pipe the flow speed is 9.15 m/s and the pipe diameter is 11.5 cm. At location 2 the pipe diameter is 17.3 cm. At location 1 the pipe is 9.89 m higher than it is at location 2. Ignoring viscosity, calculate the difference between the fluid pressure at location 2 and the fluid pressure at location 1.

Given: density of liquid x = 1.33 x 103 kg/m3,

at location1: flow speed s1 = 9.15 m/s, pipe diameter d1 = 11.5 cm = 0.115 m,

at location 2 : pipe diameter d2= 17.3 cm= 0.173 m,

The equation of continuity

The equation of continuity states that for an incompressible fluid flowing in a tube of varying cross-section, the mass flow rate is the same everywhere in the tube. The mass flow rate is simply the rate at which mass flows past a given point, so it's the total mass flowing past divided by the time interval. The equation of continuity can be reduced to:

as per given question density is constant.

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