A pump charges a sealed accumulator vessel with water ( , ) at a steady

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 pump charges a sealed accumulator vessel with water (

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

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

) at a steady

Q = 4.0\ \mathrm{L\,s^{-1}}

. The suction pipe has internal bore

80\ \mathrm{mm}

and draws from an open tank whose water surface stands

1.0\ \mathrm{m}

above the pump; a conical reducer of length

0.25\ \mathrm{m}

takes the line from

80\ \mathrm{mm}

to a delivery pipe of internal bore

50\ \mathrm{mm}

, and along that reducer the speed varies linearly with distance. The delivery pipe ends

14.0\ \mathrm{m}

above the pump, discharging into the accumulator at a point

1.5\ \mathrm{m}

below the water surface inside it; the air space above that water is at a gauge pressure of

2.5\ \mathrm{bar} = 2.5\times10^{5}\ \mathrm{Pa}

. The water inside the accumulator and in the open tank may be treated as at rest, and friction everywhere and the change of kinetic energy between suction and delivery are to be neglected. ((a)) Find the water speeds in the suction pipe and in the delivery pipe. ((b)) Find the gauge pressure at the point where the delivery pipe discharges inside the accumulator. ((c)) The pump's own inlet and outlet are at the same height, and the kinetic-energy change is neglected as stated. The pump raises the pressure from the value at its inlet (given by the head of the open tank) to the value its outlet needs to drive the water up

14.0\ \mathrm{m}

to the discharge point. Find this pressure rise

\Delta p

across the pump and the minimum pumping power,

P = Q\,\Delta p

. ((d)) The flow is steady. Find the magnitude of the acceleration of a water parcel at the small end of the reducer.

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