Concept explainers
(a)
The height difference between the surface of both water and oil in the U tube.
(a)
Answer to Problem 81AP
The height difference between the surface of both water and oil in the U tube is
Explanation of Solution
Three figures showing the three stages of the U tube is given below. The first figure shows water alone in the U tube. Figure 1 shows water in the U tube.
Consider Figure 2. The figure shows the oil and water in the tube.
Consider the left tube of the U tube which contains water.
Write the expression for pressure in the left tube.
Here,
Consider the right hand tube which contains oil.
Here,
Apply Pascal’s law. The change in pressure in any point of the fluid is equally transmitted to all points of the fluid. Here pressure at left tube equals to pressure at right tube.
Equate expressions (I) and (II) and solve for
Conclusion:
Substitute
Therefore, the height difference between the surface of both water and oil in the U tube is
(b)
The speed of the air blown across the left arm.
(b)
Answer to Problem 81AP
The speed of the air blown across the left arm is
Explanation of Solution
Right arm of the U tube is shielded by blowing air from the left arm and the levels of liquids in both the arms of tube becomes equal.
Consider Figure 3. The fluid levels in both the arms is same.
Write Bernoulli’s equation for left part and right part of the U tube.
Here,
Height of liquids in both right and left arm are equal. That is
Therefore rewrite expression (I).
Solve expression (II) to find the difference of pressure between right and left arms of the tube.
Consider points C and D which are at the same level of the oil-water interface layer of right arm.
Write the expression for the pressure at point C of left arm.
Here,
Write the expression for the pressure at point D of right arm.
Here,
By Pascal’s law,
Solve expressions (VI).
Use expression (III) in (VII) to find
Conclusion:
Substitute
Therefore, the speed of the air blown across the left arm is
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Chapter 14 Solutions
Physics For Scientists And Engineers With Modern Physics, 9th Edition, The Ohio State University
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