GATE Civil Engineering (CE) 2027 Test: Energy Equation & Its Applications

Flow of liquid through a long pipe of constant diameter at a constant rate is steady uniform flow; flow of liquid through a long pipe line of constant diameter, at either increasing or decreasing rate is unsteady-uniform flow; flow of liquid through a tapering pipe at a constant rate is steady-nonuniform flow and flow through a tapering pipe at either increasing or decreasing rate is unsteady- non-uniform flow.

The ratio of throat to inlet diameters d₂/d₁ may range between 0.75 and 0.25, but the most commonly used ratio is 0.50.
A smaller ratio gives a higher difference in the piezometric heads (between the inlet and the throat) which can be measured more accuratedly by a differential manometer. At the same time, a smaller throat (that is a lower d₂/d₁ ratio) will mean higher throat velocities which may cause pressures low enough to liberate dissolved gases thereby creating conditions for cavitation to set in.

A venturi meter is a device which is used for measuring the rate of flow of fluid through a pipe. The basic principle on which a venturi meter works in that by reducing the cross-sectional area of the flow passage, a pressure difference is created and the measurement of the pressure difference enables the determination of the discharge through the pipe.

At vena-contracta velocity of fluid is maximum at stagnation point velocity is zero and all kinetic energy is converted to pressure energy.

The equation is Bernoulli’s equation. It is based on following assumptions:
(i) flow is steady
(ii) fluid is incompressible
(iii) fluid is. non-viscous since viscous force has been neglected; and
(iv) it is applicable to points along a streamline

For an orifice the coefficient of discharge C_d, coefficient of velocity C_v and coefficient of contraction C_c is related as,
C_d = C_c x C_v

C_d = (0.75)² x 0.98