Water pressurized to 4 × 10⁵ Pa is flowing at 5.0 m/s in a pipe which contracts to 1/3 of its former area.What are the pressure and speed of the water after the contraction? (density of water = 1 × 10³ kg/m³) A) 2 × 10⁵ Pa,15 m/s B) 3 × 10⁵ Pa,10 m/s C) 3 × 10⁵ Pa,15 m/s D) 4 × 10⁵ Pa,1.5 m/s

Question

Quizplus · Accepted Answer

Using the conservation of mass equation, A1V1 = A2V2, where A is the cross-sectional area and V is the velocity of water, we can find the speed of water after the contraction:
A1V1 = A2V2
(1/3)A1V1 = A2(5.0 m/s)
V2 = (1/3)V1

Using Bernoulli's equation, P + (1/2)ρv^2 = constant, where P is the pressure and ρ is the density of water, we can find the pressure of water after the contraction:
P1 + (1/2)ρv1^2 = P2 + (1/2)ρv2^2
P1 + (1/2)ρ(5.0 m/s)^2 = P2 + (1/2)ρ[(1/3)V1]^2
P1 - P2 = (1/2)ρ[(1/9)V1^2 - 25]

Substituting the given values and solving for P2:
P2 = P1 - (1/2)ρ[(1/9)(5.0 m/s)^2 - 25]
P2 = 3 × 10^15 Pa

Therefore, the pressure and speed of the water after the contraction are 3 × 10^15 Pa and 15 m/s, respectively. The correct answer is choice C.

Water Pressurized to 4 × 105 Pa Is Flowing at 5.0

Water Pressurized to 4 × 10⁵ Pa Is Flowing at 5.0