Water flows steadily through a horizontal pipe that tapers from a diameter of 0.20 m at the wide end to 0.10 m at the narrow end over a length of 2.0 m. The volumetric flow rate is $0.015\,\text{m}^{3}\text{s}^{-1}$. Assume incompressible, inviscid flow.

(a) Using Bernoulli's equation, calculate the pressure difference between the wide and narrow sections of the pipe.
(b) If the pressure at the wide end is maintained 150 kPa above atmospheric pressure, determine the power that must be supplied by a pump to sustain the flow.

Question

Water flows steadily through a horizontal pipe that tapers from a diameter of 0.20 m at the wide end to 0.10 m at the narrow end over a length of 2.0 m. The volumetric flow rate is $0.015\,\text{m}^{3}\text{s}^{-1}$. Assume incompressible, inviscid flow.

(a) Using Bernoulli's equation, calculate the pressure difference between the wide and narrow sections of the pipe.
(b) If the pressure at the wide end is maintained 150 kPa above atmospheric pressure, determine the power that must be supplied by a pump to sustain the flow.

Accepted Answer

(a) ≈ 1.7 kPa pressure drop (wide → narrow); (b) pump power ≈ 2.3 kW

Gce Model Questions Vol1 2022 Physics Question 20

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