Water flows through a horizontal pipe of cross-sectional area 10. cm at a pressure of 0.25 atm.The flow rate is 1.0 L/s. At a valve, the effective cross-sectional area of the pipe is reduced to 5.0cm2. What is the pressure at the valve?A) 0.112 atmB) 7.7 x 103 PaC) 0.157 atmD) 0.200 atmE) 0.235 atm

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Asked Dec 1, 2019
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Water flows through a horizontal pipe of cross-sectional area 10. cm at a pressure of 0.25 atm.
The flow rate is 1.0 L/s. At a valve, the effective cross-sectional area of the pipe is reduced to 5.0
cm2. What is the pressure at the valve?
A) 0.112 atm
B) 7.7 x 103 Pa
C) 0.157 atm
D) 0.200 atm
E) 0.235 atm
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Water flows through a horizontal pipe of cross-sectional area 10. cm at a pressure of 0.25 atm. The flow rate is 1.0 L/s. At a valve, the effective cross-sectional area of the pipe is reduced to 5.0 cm2. What is the pressure at the valve? A) 0.112 atm B) 7.7 x 103 Pa C) 0.157 atm D) 0.200 atm E) 0.235 atm

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Expert Answer

Step 1

Since, the density of water is 103 kg/m3.

Summarizing the given values,

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1 L/s 10 m3/s A 10 cm2 -10x10~m2 A 5 cm2 =5x 10m2 P 0.25 atm0.25 x1.013 x 10° Pa = 0.25 x 10' Pa p 10 kg/m3

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Step 2

Now, for velocity of water v1 which flows through a horizontal pipe of cross-sectional area A1.

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105 AvQ 103 m3/s (10x10 m2 )v; = 1 m/s

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Step 3

From the equation of continuity, the rate of incompressible fluid (Q) remains constant.

Now, for velocity of water v2...

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