An ideal fluid,of density 0.90 × 10³ kg/m³,flows at 5.0 m/s through a level pipe with radius of 0.5 cm.The pressure in the fluid is 1.3 × 10⁵ N/m².This pipe connects to a second level pipe,with radius of 1.4 cm.Find the speed of flow in the second pipe. A) 39.2 m/s B) 1.79 m/s C) 0.64 m/s D) 14 m/s E) 5.13 m/s

Question

Quizplus · Accepted Answer

We can apply the principle of continuity (Av = constant) to determine the speed of flow in the second pipe. Since the fluid is ideal, we can also apply Bernoulli's equation (P + 1/2pv^2 = constant) to relate the pressure and velocity of the fluid.

Using the given values for the first pipe, we have:

A1 = π(0.5 cm)^2 = 0.785 cm^2
v1 = 5.0 m/s
ρ = 0.90 × 10^3 kg/m^3
P1 = 1.3 × 10^5 N/m^2

From Bernoulli's equation, we can write:

P1 + 1/2ρv1^2 = P2 + 1/2ρv2^2

Solving for v2, we get:

v2 = sqrt(2(P1 - P2)/ρ + v1^2) = 0.64 m/s

Therefore, the answer is C).

An Ideal Fluid,of Density 0