Concept explainers
A section of pipe with an internal diameter of 10.0 cm tapers to an inner diameter of 6.00 cm as it rises through a height of 1.70 m at an angle of 60.0° with respect to the horizontal. The pipe carries water and its higher end is open to air. (a) If the speed of the water at the lower point is 15.0 cm/s, what are the pressure at the lower end and the speed of the water as it exits the pipe? (b) If the higher end of the pipe is 0.300 m above ground, at what horizontal distance from the pipe out let does the water land?
(a)
The pressure at the lower end and the speed of the water as it exits the pipe.
Answer to Problem 117P
The pressure at the lower end is
Explanation of Solution
Take point 1 to be the lower end and the point 2 to be upper end of the pipe.
Write the continuity equation of fluids.
Here,
Rewrite the above equation for
Write the equation for
Here,
Write the equation for
Here,
Put the above two equations in equation (II).
Write the Bernoulli’s equation.
Here,
Substitute
Here,
Conclusion:
The atmospheric pressure is
Substitute
Substitute
Therefore, the pressure at the lower end is
(b)
The horizontal distance from the pipe outlet where the water lands.
Answer to Problem 117P
The horizontal distance from the pipe outlet where the water lands is
Explanation of Solution
Write the equation for the horizontal distance from the pipe outlet where the water lands.
Here,
Write the equation for
Here,
Put the above equation in equation (V).
Write the equation for the vertical distance through which the water falls.
Here,
The value of
Substitute
Write the equation for
Put the above equation in equation (VII).
The above equation is a quadratic equation in
Write the equation for the root of the above quadratic equation.
Conclusion:
Substitute
Time cannot be negative.
Substitute
Therefore, the horizontal distance from the pipe outlet where the water lands is
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Chapter 9 Solutions
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