A horizontal water pipe of internal diameter mm carries a steady flow through a…
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 Bernoulli at work: Venturi meters, Pitot tubes and lift
Problem
A horizontal water pipe of internal diameter 80 mm carries a steady flow through a Venturi contraction whose throat diameter is 40 mm. The flow rate is measured independently by collecting the discharge in a tank: 22.0 kg of water arrives in 10.0 s. Take the water as incompressible with density 1000 kg m−3, and treat the flow as steady, inviscid and along the axial streamline.
((a)) Apply the steady integral mass balance ∮Sρu⋅ndS=0 to a control volume bounded by the pipe wall, a cross-section in the wide pipe and a cross-section at the throat, to find the mean speed in the wide pipe and the mean speed at the throat.
((b)) Hence find the pressure drop from the wide pipe to the throat.
((c)) A small Pitot-static tube is placed on the axis at the throat, its nose facing upstream and its ring of static holes a little way back along its own body, where they read the static pressure of the throat. What pressure difference does its gauge read?