A 7.0-cm-diameter horizontal pipe gradually narrows to 5.0 cm . When water flows through this pipe at a certain rate, the gauge pressure in these two sections is 32.0 kPa and 25.0 kPa , respectively.
What is the volume rate of flow?
Express your answer using two significant figures.
radius of the 7 cm pipe, r1 = 7/2 = 3.5 cm
radius of pipe, r2 = 5/2 = 2.5 cm
let the speed of the flow is v1 and v2
Using equation of continuity
pi * 3.5^2 * v1 = pi * 2.5^2 * v2
Using Bernoulli's equation
P1 + 0.50 * p * v1^2 = P2 + 0.50 * p * v2^2
32000 + 0.50 * 1000 * v1^2 = 25000 + 0.50 * 1000 * v2^2
solving for v1 and v2
v1 = 2.22 m/s
v2 = 4.35 m/s
volume flow rate = pi * r1^2 * v1
volume flow rate = pi * 0.035^2 * 2.22
volume flow rate = 0.0085 m^3/s
the volume flow rate is 0.0085 m3/s
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