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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 5.25 105 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
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 5.25 105 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
Thegauge pressureathouseA, and B, is the measurement of pressurerelativeto the pressure of theatmosphere.The gauge pressure at houseAis approximately244.5 kPa.The gauge pressure at houseBis approximately173.116 kPa.Reasons:Question parameters;Mass of waterin the tower, m =5.25 × 10⁵ kgShape of the reservoir =SphericalHeight of thebottomof the reservoir above the main ground level = 15.0 mHeightof the houseAabove the ground = 0Height of thehouse Babove the ground = 7.30 m(a)Required:The gauge pressure at house ASolution:Thedensityof thewater, ρ ≈997 kg/m³Volumeof water in thefilled tank= Volume of the tank ≈ 526.28 m³Therefore;Which gives;The diameter of the tank = The height of the tank, h = 2 × r∴ h = 2 × 5 m =10 mThe gauge pressure is the pressure above theprevailing atmosphericpressure;For the system vented to the atmosphere,= ρ·g·hTherefore;The gauge pressure at houseA,=997 × 9.81 × (10 + 15)= 244514.25The gauge pressure at houseA,= 244514.25 N/m² ≈ 244.5 kPa(b) Required:Gauge pressure at house BAt house B, we have;Gauge pressure at houseB,=997 × 9.81 × (10 + 15 - 7.3)= 173116.089The gauge pressure at house B = 173116.089 N/m² ≈173.116 kPaLearn more here:brainly.com/question/20709159...