A horizontal pipe of 50 cm² cross-sectional area carries a fluid of unknown density at a speed of 3.0 m/s.This pipe feeds a smaller pipe of cross section 25 cm².If the pressure difference between the two sections of pipe is 9000 Pa,find the density of the fluid. A)500 kg/m³ B)360 kg/m³ C)6000 kg/m³ D)720 kg/m³ E)Cannot solve,not enough information given

Question

Quizplus · Accepted Answer

We can use the equation of continuity to relate the velocities of the fluids in the two pipes, and then use Bernoulli's equation to find the density of the fluid. The equation of continuity states that the volume flow rate of the fluid is constant, which means:

A1V1 = A2V2

where A1 and V1 are the cross-sectional area and velocity of the fluid in the larger pipe, and A2 and V2 are the corresponding values for the smaller pipe. Substituting the given values, we get:

(0.5 m^2)(3.0 m/s) = (0.25 m^2)V2

Solving for V2, we get:

V2 = 6.0 m/s

Now, applying Bernoulli's equation between the two sections of pipe, we have:

P1 + (1/2)ρV1^2 = P2 + (1/2)ρV2^2

where P1 and V1 are the pressure and velocity of the fluid in the larger pipe, and P2 is the pressure of the fluid in the smaller pipe (since the velocity is now V2).

Substituting the given values and solving for ρ, we get:

ρ = (P2 - P1)/(V2^2 - V1^2) = 720 kg/m^3

Therefore, the answer is D (720 kg/m^3).

A Horizontal Pipe of 50 Cm2 Cross-Sectional Area Carries a Fluid

A Horizontal Pipe of 50 Cm² Cross-Sectional Area Carries a Fluid