Water flows through a horizontal pipe of cross-sectional area 10.0 cm² at a pressure of 0.250 atm with a flow rate is 1.00 L/s.At a valve,the effective cross-sectional area of the pipe is reduced to 5.00 cm².What is the pressure at the valve? The density of water is 1000 kg/m³,and treat it as an ideal incompressible fluid. A)0.110 atm B)0.235 atm C)0.200 atm D)0.157 atm E)7700 Pa

Question

Quizplus · Accepted Answer

We can use the principle of continuity to find the velocity of water before and after the valve:
A1v1 = A2v2
where A1 = 10.0 cm^2 = 0.001 m^2, A2 = 5.00 cm^2 = 0.0005 m^2, v1 = Q/A1 = 0.1 m/s, and Q = 1.00 L/s = 0.001 m^3/s.
So, v2 = (A1/A2)v1 = 0.2 m/s.

Next, we can use Bernoulli's equation to relate the pressure at the two points:
P1 + 1/2ρv1^2 = P2 + 1/2ρv2^2
where P1 = 0.250 atm = 25398.8 Pa and ρ = 1000 kg/m^3.
Solving for P2, we get:
P2 = P1 + 1/2ρ(v1^2 - v2^2) = 0.235 atm = 23912.9 Pa.
Therefore, the pressure at the valve is B) 0.235 atm.

Water Flows Through a Horizontal Pipe of Cross-Sectional Area 10