Concept explainers
(a)
The speed at which the water leaves the faucet.
(a)
Answer to Problem 69P
The speed at which the water leaves the faucet is
Explanation of Solution
Write the equation for the volume flow rate.
Here,
Write the equation for the volume flow rate in terms of the speed of the water.
Here,
Rewrite the above equation for
Write the equation for
Here,
Put the above equation in equation (II).
Conclusion:
Substitute
Substitute
Therefore, the speed at which the water leaves the faucet is
(b)
The gauge pressure in the
(b)
Answer to Problem 69P
The gauge pressure in the
Explanation of Solution
Take point 1 to be in the entrance pipe and point 2 to be at the faucet 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 (IV).
Write the Bernoulli’s equation.
Here,
Rearrange the above equation.
Write the equation for gauge pressure.
Here,
Put the above equation in equation (VI).
Conclusion:
The density of water is
Substitute
Substitute
Therefore, the gauge pressure in the
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Chapter 15 Solutions
Principles of Physics: A Calculus-Based Text
- Water is moving at a velocity of 2.00 m/s through a hose with an internal diameter of 1.60 cm. (a) What is the flow rate in liters per second? (b) The fluid velocity in this hose's nozzle is 15.0 m/s. What is the nozzle's inside diameter?arrow_forwardThe water supply of a building is fed through a main pipe 6.00 cm in diameter. A 2.00-cm-diameter faucet tap, located 2.00 m above the main pipe, is observed to fill a 25.0-L container in 30.0 s. (a) What is the speed at which the water leaves the faucet? (b) What is the gauge pressure in the 6-cm main pipe? Assume the faucet is the only leak in the building.arrow_forwardWater is moving at a velocity of 2.00 m/s through a hose with internal diameter of 1.60 cm. (a) What is the flow rate in liters per second? (b) The fluid velocity in this hose's nozzle is 15.0 m/s. What is the nozzle's inside diameter?arrow_forward
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- Liquid toxic waste with a density of 1752 kg/m3 is flowing through a section of pipe with a radius of 0.312 m at a velocity of 1.64 m/s. a. What is the velocity of the waste after it goes through a constriction and enters a second section of pipe with a radius of 0.222 m? b. If the waste is under a pressure of 850,000 Pa in the first section of pipe, what is the pressure in the second (constricted) section of pipe?arrow_forwardHow tall must a water-filled manometer be to measure blood pressures as high as 300 mm Hg?arrow_forwardFigure P15.52 shows a Venturi meter, which may be used to measure the speed of a fluid. It consists of a Venturi tube through which the fluid moves and a manometer used to measure the pressure difference between regions 1 and 2. The fluid of density tube moves from left to right in the Venturi tube. Its speed in region 1 is v1, and its speed in region 2 is v2. The necks cross-sectional area is A2, and the cross-sectional area of the rest of the tube is A1. The manometer contains a fluid of density mano. a. Do you expect the fluid to be higher on the left side or the right side of the manometer? b. The speed v2 of the fluid in the neck comes from measuring the difference between the heights (yR yL) of the fluid on the two sides of manometer. Derive an expression for v2 in terms of (yR yL), A1, A2, tube, and mano. FIGURE P15.52arrow_forward
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