A dewatering pump stands at the bottom of a mine shaft with its intake below the…

PHYSICS · Multi-part · Fermi University Physics · Fluids & Continuum Physics · Kinematics, conservation laws and ideal flow · Kinematics, conservation laws and ideal flow

Fluids and Continuum Physics, Ch Conservation of mass, momentum and energy

Problem

A dewatering pump stands at the bottom of a mine shaft with its intake

1.2\ \mathrm{m}

below the still surface of the sump. It delivers water (

\rho = 1000\ \mathrm{kg\,m^{-3}}

g = 9.8\ \mathrm{m\,s^{-2}}

) at a steady

Q = 12\ \mathrm{L\,s^{-1}}

up a rising main of internal bore

100\ \mathrm{mm}

, which ends in a nozzle of exit bore

40\ \mathrm{mm}

discharging as a free jet into an open channel

45.0\ \mathrm{m}

above the sump surface. The nozzle taper is

0.15\ \mathrm{m}

long and the speed varies linearly with distance along it. The sump surface is open to the atmosphere at

1.013\times10^{5}\ \mathrm{Pa}

. Pipe friction is to be neglected. ((a)) Find the speed of the jet leaving the nozzle, and the speed in the rising main. ((b)) Before the pump starts, with the water everywhere at rest, find the absolute pressure at the pump intake. ((c)) Taking the still sump surface as datum, find the minimum pumping power: the rate at which the pump must supply gravitational potential energy for the

45.0\ \mathrm{m}

lift plus the rate at which kinetic energy leaves in the jet. ((d)) The flow is steady. Find the magnitude of the acceleration of a water parcel at the nozzle exit.

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