An incompressible fluid is flowing through a horizontal pipe with a constriction. The velocity of the fluid in the wide section of the pipe is 4.00 m/s and the velocity of the fluid in the narrow section of pipe is 9.00 m/s. The pressure of the fluid in the wide section is 250 kPa. What is the pressure in the narrow section of the pipe? (density of the fluid is 1,000 kg/m³) A) 218 kPa B) 225 kPa C) 237 kPa D) 246 kPa E) 252 kPa

Question

Quizplus · Accepted Answer

Using Bernoulli's equation for incompressible flow, $P_1 + \frac{1}{2}\rho v_1^2 = P_2 + \frac{1}{2}\rho v_2^2$, where $P_1$ and $P_2$ are the pressures, $v_1$ and $v_2$ are the velocities, and $\rho$ is the density of the fluid. Solving for $P_2$, we get $P_2 = P_1 + \frac{1}{2}\rho(v_1^2 - v_2^2)$. Substituting the given values, $P_2 = 250,000 + \frac{1}{2}(1000)(4^2 - 9^2) = 250,000 - 32,500 = 217,500$ Pa or 218 kPa.

An Incompressible Fluid Is Flowing Through a Horizontal Pipe with a Constriction