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Fluid Flows

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An ideal fluid flows through a pipe of circular cross section of radius r at a speed v_(0) . Now a viscous liquid is made to flow through the pipe at the same volume flow rate (measured in m^(3)s^(–1) ). Find the maximum speed of a fluid particle in the pipe.

The loss of pressure when a fluid flows through a pipe is give by P = krho^(a)l V^(b)d^(c) mu where d and l are diameter and length of the pipe respectively, rho,d and mu are the mass, density and coefficient of viscosity of the fluid, V is the mean velocity of flow through the pipe and k is a numerical constant. Find the values of a, b and c.

A non-viscous liquid of constant density 500 kg//m^(3) flows in a variable cross-sectional tube. The area of cross section of the tube at two points P and Q at heights of 3 m and 6 m are 2 xx 10^(-3) m^(3) and 4 xx 10^(-3) m^(3) , respectively. Find the work done per unit volume by the forces of gravity as the fluid flows from point P to Q .

A non-viscous liquid of constant density 1000kg//m^3 flows in a streamline motion along a tube of variable cross section. The tube is kept inclined in the vertical plane as shown in Figure. The area of cross section of the tube two point P and Q at heights of 2 metres and 5 metres are respectively 4xx10^-3m^2 and 8xx10^-3m^2 . The velocity of the liquid at point P is 1m//s . Find the work done per unit volume by the pressure and the gravity forces as the fluid flows from point P to Q.

An application of Bernoulli's equation for fluid flow is found in