Most towns use a water tower to store water and provide pressure in the pipes that deliver water to customers. The figure below shows a spherical water tank that holds 6.00 105 kg of water when full. Note that the tank is vented to the atmosphere at the top and that the pipe delivering water to customer Smith is a height h = 7.00 m above the level of the pipe delivering water to customer Jones. Determine the gauge pressure of the water at the faucet of each house when the tank if full. (a) Jones house Pa(b) Smith house Pa This diagram illustrates a simple water distribution system involving a water tower and two residential houses, designated as the Smith house and the Jones house.- **Water Tower**: At the center of the diagram is a large, spherical water tower. The water tower is elevated at a height of 18.0 meters above the ground and is equipped with a vent at the top.- **Piping System**: The water flows through a network of pipes from the tower to each of the houses. The pipes are depicted in blue.- **Smith House**: On the left side of the diagram is the Smith house, which receives water through a pipe connected from the water tower. There is an elevation difference marked as \( h \) between the ground and where the pipe enters the house. A faucet is shown as the point where water is accessed.- **Jones House**: On the right side of the diagram is the Jones house. This house is also connected to the water tower through a pipeline that runs underground. A faucet is similarly depicted as the point of use.Overall, the diagram represents the concept of water pressure and distribution using gravity from an elevated source (the water tower) to supply water to residential homes.

Name: Most towns use a water tower to store water and provide pressure in th
Uploaded: 2024-03-20T06:51:10.000Z
Channel: Bartleby
Description: Most towns use a water tower to store water and provide pressure in the pipes that deliver water to customers. The figure below shows a spherical water tank that holds 6.00 105 kg of water when full. Note that the tank is vented to the atmosphere at

Given data: Mass of the water, m=6.00×105 kg Height of the Smith’s house, h=7.00 m H=18.0 m Density of water, ρ=1000 kg/m3Radius of the spherical water tank can be calculated by the help of density formula: ρ=mV=m43πr3 ∴ r3=m43πρ r=m43πρ3 Plugging in the given values: r=6.00×10543×3.14×100013 =5.23 m (a) Height of faucet from the jones house to the top of the tank: HJ=2r+18.0 =2×5.23+18.0 =28.46 m Gauge pressure at the faucet of Jones house, PJ=ρgHJ =1000×9.8×28.46 =278908 Pa (b) Height of faucet from the Smith house to the top of the tank: HS=2r+18.0-h =2×5.23+18.0-7 =21.46 m Gauge pressure at the faucet of Smith house: PS=ρgHS =1000×9.8×21.46 =210308 Pa Answer: Gauge Pressure at Jones house: 278908 Pa Gauge pressure at Smith house: 210308 Pa