An incompressible fluid of density rho flows steadily through a horizontal pipe of changing cross-section. At a point where the pressure is P the fluid speed is v. At another point where the pressure is P/2 the speed is V. For streamline flow, V equals:

sqrt(P/(2*rho) + v²)
sqrt(P/rho + v²)
sqrt(2*P/rho + v²)
sqrt(P/rho + v)

Correct answer: sqrt(P/rho + v²)

Solution

Bernoulli's principle for a horizontal pipe states the sum of pressure and kinetic energy per unit volume is constant. Solving for V gives the result.

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