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 6.00 m/s and the velocity of the fluid in the narrow section of pipe is 8.00 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) 183 kPa B) 236 kPa C) 268 kPa D) 285 kPa E) 298 kPa

Question

Quizplus · Accepted Answer

The pressure in the narrow section can be found using Bernoulli's equation, which states that the total mechanical energy in a flowing fluid remains constant. The equation is $P_1 + \frac{1}{2}\rho v_1^2 = P_2 + \frac{1}{2}\rho v_2^2$, where $P_1$ and $P_2$ are the pressures in the wide and narrow sections, $v_1$ and $v_2$ are the velocities in the wide and narrow sections, 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, $P_2 = 250,000 + \frac{1}{2}(1000)(6^2 - 8^2) = 250,000 - 14,000 = 236,000$ Pa or 236 kPa.

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