A fluid is flowing through a horizontal pipe of varying cross-section, with speed v ms−1 at a point where the pressure is P Pascal. At another point where pressure is P/2 Pascal its speed is V ms−1. If the density of the fluid is ρ kg m−3 and the flow is streamline, then V is equal to:

Question

Accepted Answer

√(P/ρ + v²). For horizontal streamline flow, P + (1/2)rho v^2 = (P/2) + (1/2)rho V^2. So (1/2)rho(V^2 - v^2) = P - P/2 = P/2, giving V^2 = v^2 + P/rho, i.e. V = sqrt(P/rho + v^2).

A fluid is flowing through a horizontal pipe of varying cross-section, with speed v ms−1 at a point where the pressure is P Pascal. At another point where pressure is P/2 Pascal its speed is V ms−1. If the density of the fluid is ρ kg m−3 and the flow is streamline, then V is equal to:

Solution

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