An incompressible fluid is flowing through a pipe with a constriction. The pipe is on an incline with an angle of 20.0 degrees. The narrow section is 15.0 m from the wide section and the narrow section is lower than the wide section. 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 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) 278 kPa B) 228 kPa C) 195 kPa D) 167 kPa E) 145 kPa

Question

Quizplus · Accepted Answer

Explanation:Using Bernoulli's equation, we have:P1 + 1/2 * ρ * v1^2 + ρ * g * h1 = P2 + 1/2 * ρ * v2^2 + ρ * g * h2where P1 and v1 are the pressure and velocity in the wide section, P2 and v2 are the pressure and velocity in the narrow section, ρ is the density of the fluid, g is the acceleration due to gravity, and h1 and h2 are the heights of the wide and narrow sections, respectively.We can simplify this equation by noting that h2 - h1 = 15.0 m * sin(20.0°) = 5.19 m. Substituting this into the equation, we get:P1 + 1/2 * ρ * v1^2 = P2 + 1/2 * ρ * v2^2 + ρ * g * 5.19 mPlugging in the given values, we get:250 kPa + 1/2 * 1000 kg/m^3 * (6.00 m/s)^2 = P2 + 1/2 * 1000 kg/m^3 * (9.00 m/s)^2 + 1000 kg/m^3 * 9.81 m/s^2 * 5.19 mSolving for P2, we get:P2 = 278 kPa

An Incompressible Fluid Is Flowing Through a Pipe with a Constriction