An incompressible fluid is flowing through a pipe with a constriction. The pipe is on an incline with an angle of 30.0 degrees from the horizontal. The narrow section is 10.0 m from the wide section and the narrow section is higher than the wide section. 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) 169 kPa B) 175 kPa C) 180 kPa D) 193 kPa E) 205 kPa

Question

Quizplus · Accepted Answer

To find the pressure in the narrow section, we can use the Bernoulli's equation, which for an incompressible fluid is given by $P_1 + \frac{1}{2}\rho v_1^2 + \rho gh_1 = P_2 + \frac{1}{2}\rho v_2^2 + \rho gh_2$. Given the incline and the height difference, we can calculate $h_2 - h_1 = 10 \sin(30^\circ) = 5 \, \text{m}$. Substituting the given values and solving for $P_2$, we find that the pressure in the narrow section is 169 kPa.

An Incompressible Fluid Is Flowing Through a Pipe with a Constriction