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College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300

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BuyFindarrow_forward

College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300
Textbook Problem

The inside diameters of the larger portions of the horizontal pipe depicted in Figure P9.45 are 2.50 era. Water flows to the right at a rate of 1.80 × 10−4 m3/s. Determine the inside diameter of the constriction.

images

Figure P9.45

To determine
The inside diameter of the constriction.

Explanation

Section1:

To determine: The flow speed of water inside the larger section.

Answer: The flow speed of water inside the larger section is 0.367m/s .

Explanation: The flow speed of water inside of the larger section is calculated using continuity equation as follows. A1v1=flowratev1=flowrate/A1=4(flowrate)/πd12 .

Given info: The flow speed of water is 1.80×104m3/s and the inside diameter of the larger section of the pipe is 2.50cm .

The formula for the flow speed of water inside the larger section of the water is,

v1=4(flowrate)πd12 .

  • d1 is inside diameter of the larger section.

Substitute 1.80×104m3/s for flowrate and 2.50cm for d1 to find v1 .

v1=4(1.80×104m3/s)(3.14)[(2.50cm)(0.01m1cm)]2=0.367m/s

Thus, the flow speed of water inside the larger section is 0.367m/s .

Section2:

To determine: The cross sectional area of the constriction.

Answer: The cross sectional area of the constriction is 1.70×104m2 .

Explanation: We use Bernoulli’s equation for the flow speed of water in the region of that constriction such that v22=v12+(2/ρ)(P1P2) by assuming that y1=y2 . The pressure difference between these two regions would be P1P2=Patm+ρgh1Patm+ρgh2=ρg(h1h2) which going to be substituted in the expression of the flow speed of the water in constriction region is v2=v12+2g(h1h2) .

Now we arrive that the area of constriction is A2=flowrate/v2=flowrate/(v12+2g(h1h2)) .

Given info: The flow speed of water in the larger section of the pipe is 0.367m/s , acceleration due to gravity is 9.80m/s2 , the water level in the left most stand pipe is 10

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