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A water tower is a familiar sight in many towns. The purpose of such a tower is to provide storage capacity and to provide sufficient pressure in the pipes that deliver the water to customers. The drawing shows a spherical reservoir that contains 6.85 x 105 kg of water when full. The reservoir is vented to the atmosphere at the top. For a full reservoir, find the gauge pressure that the water has at the faucet in (a) house A and (b) house B. Ignore the diameter of the delivery pipes. The drawing shows a hydraulic chamber with a spring (spring constant = 1140 N/m) attached to the input piston and a rock of mass 37.0 kg resting on the output plunger. The piston and plunger are nearly at the same height, and each has a negligible mass. (c) By how much is the spring compressed from its unstrained position?

A water tower is a familiar sight in many towns. The purpose of such a tower is to provide storage capacity and to provide sufficient pressure in the pipes that deliver the water to customers. The drawing shows a spherical reservoir that contains 6.85 x 105 kg of water when full. The reservoir is vented to the atmosphere at the top. For a full reservoir, find the gauge pressure that the water has at the faucet in (a) house A and (b) house B. Ignore the diameter of the delivery pipes. The drawing shows a hydraulic chamber with a spring (spring constant = 1140 N/m) attached to the input piston and a rock of mass 37.0 kg resting on the output plunger. The piston and plunger are nearly at the same height, and each has a negligible mass. (c) By how much is the spring compressed from its unstrained position?

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A water tower is a familiar sight in many towns. The purpose of such a tower is to provide storage capacity and to provide sufficient pressure in the pipes that deliver the water to customers. The drawing shows a spherical reservoir that contains 6.85 x 105 kg of water when full. The reservoir is vented to the atmosphere at the top. For a full reservoir, find the gauge pressure that the water has at the faucet in (a) house A and (b) house B. Ignore the diameter of the delivery pipes.

The drawing shows a hydraulic chamber with a spring (spring constant = 1140 N/m) attached to the input piston and a rock of mass 37.0 kg resting on the output plunger. The piston and plunger are nearly at the same height, and each has a negligible mass. (c) By how much is the spring compressed from its unstrained position?

### Understanding Water Towers and Pressure A water tower is commonly used in towns to store water and ensure adequate pressure in the pipes that supply water to customers. This illustration depicts a spherical reservoir containing 6.85 x 10^5 kg of water when full. The reservoir is open to the atmosphere through a vent at the top. **Objective:** Determine the gauge pressure of the water at: - (a) Faucet in house A - (b) Faucet in house B **Diagram Explanation:** - **Reservoir:** Shown as a blue sphere on a stand, 15.0 meters above the ground. - **Vent:** At the top of the reservoir for atmospheric exchange. - **House A:** Located directly to the right of the tower, with a faucet at ground level. - **House B:** Positioned to the left of the tower, with a faucet 7.30 meters above the ground level. **Instructions:** - Assume negligible pipe diameter. - Use the provided height differences to calculate pressures at the faucets. **Calculations:** For both (a) and (b), insert the gauge pressure values in the respective fields: - (a) __________ Units - (b) __________ Units Use the principles of fluid statics and the given details to solve the problem. Gauge pressure reflects the pressure relative to atmospheric pressure.
Transcribed Image Text:### Understanding Water Towers and Pressure A water tower is commonly used in towns to store water and ensure adequate pressure in the pipes that supply water to customers. This illustration depicts a spherical reservoir containing 6.85 x 10^5 kg of water when full. The reservoir is open to the atmosphere through a vent at the top. **Objective:** Determine the gauge pressure of the water at: - (a) Faucet in house A - (b) Faucet in house B **Diagram Explanation:** - **Reservoir:** Shown as a blue sphere on a stand, 15.0 meters above the ground. - **Vent:** At the top of the reservoir for atmospheric exchange. - **House A:** Located directly to the right of the tower, with a faucet at ground level. - **House B:** Positioned to the left of the tower, with a faucet 7.30 meters above the ground level. **Instructions:** - Assume negligible pipe diameter. - Use the provided height differences to calculate pressures at the faucets. **Calculations:** For both (a) and (b), insert the gauge pressure values in the respective fields: - (a) __________ Units - (b) __________ Units Use the principles of fluid statics and the given details to solve the problem. Gauge pressure reflects the pressure relative to atmospheric pressure.
The drawing shows a hydraulic chamber with a spring (spring constant = 1140 N/m) attached to the input piston and a rock of mass 37.0 kg resting on the output plunger. The piston and plunger are nearly at the same height, and each has a negligible mass. By how much is the spring compressed from its unstrained position? **Diagram Explanation:** - The diagram features a hydraulic chamber divided into two sections by a vertical line representing a piston on the left and a plunger on the right. - Above the piston, a spring is illustrated, compressed by the piston. - The area of the piston is indicated as 15 cm². - On the right, a rock rests on the plunger, with the plunger area shown as 65 cm². - The liquid inside the chamber is colored blue, showing an equal level on both sides, signifying that the system is at equilibrium. **Question:** Calculate the amount by which the spring is compressed, represented by the variable 'x' in the equation box provided.
Transcribed Image Text:The drawing shows a hydraulic chamber with a spring (spring constant = 1140 N/m) attached to the input piston and a rock of mass 37.0 kg resting on the output plunger. The piston and plunger are nearly at the same height, and each has a negligible mass. By how much is the spring compressed from its unstrained position? **Diagram Explanation:** - The diagram features a hydraulic chamber divided into two sections by a vertical line representing a piston on the left and a plunger on the right. - Above the piston, a spring is illustrated, compressed by the piston. - The area of the piston is indicated as 15 cm². - On the right, a rock rests on the plunger, with the plunger area shown as 65 cm². - The liquid inside the chamber is colored blue, showing an equal level on both sides, signifying that the system is at equilibrium. **Question:** Calculate the amount by which the spring is compressed, represented by the variable 'x' in the equation box provided.
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