A liquid of density 1.31×10^3 kg/m3 flows steadily through a pipe of varying dia

Question

A liquid of density 1.31×10^3 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 10.7 cm. At location 2 the pipe diameter is 16.1 cm. At location 1 the pipe is 8.27 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.

A liquid of densty 1,31 x10' kgm3 nows steadily through a pipe of varying diameter and height Al location 1 along the pipe the flow speed is 9.15 m's and the pipe diameter is 10.7 cm. At location 2 the pipe diameler is 161. At location 1 the pipe is 8.27 m higher than it is at location 2 Ignoring viscosity, calculate the ditterence between the fluid pressure at location 2 and the fluid pressure at locatian 1 10.7 cm 8.27 m Pa 16.1 em

Explanation / Answer

- In fluid dynamics, for a non conducting fluid, an increase in the speed of the fluid occurs simultaneously with a decrease in pressure or a decrease in the fluid's potential energy. This is Bernoulli's principle

Use Bernoulli's equation and applying that at pipe 1,

P2/(density of liquid) + z2 + (v22)/(2g) = P1/(density of liquid) + z1 + (v12)/(2g)

Re-arranging:

P2 - P1 = (density of liquid) * ((v12 - v22)/2g + z1 - z2)

P2 - P1 = (1.31 * 103 kg/m3) * ((9.15 m/s)2 - (4.1 m/s)2)/(2*9.81 m/s2) - 8.27 m)

P2 - P1 = -6.1 kPa

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