What is the water pressure at house a and house b in this physics problem?
The drawing shows a spherical reservoir that contains 4.70 x 10^5 kg of water when full. (height of house b above ground = 7.40 m.) 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 each house. Ignore the diameter of the delivery pipes. The cylinder base that holds up the sphere of the tower is 15m tall.
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house b is 15–7.4 = 7.6 metes below the tank bottom. but we have to calculate the size of the tank to get the height of the water to the top of the tank.
density of water at 20C = 998 kg/m³
4.7e5 kg has a volume of:
4.7e5 kg / 998 kg/m³ = 471 m³
Volume of a sphere is V = ⁴/₃πr³
471 = ⁴/₃πr³
r = 4.83 meters.
d = 9.65 meters
adding that to the 7.6, we get 17.25 meters.
now to convert to pascals, which is the weight of a column of water 1 m² in area cross section.
So we have a volume of water 1 m² x 17.25 m = 17.25 m³
using the density number, that is a weight/mass of
998 kg/m³ x 17.25 m³ = 17210 kg
converting to newtons, that is 169000 newtons, which corresponds to a pressure of 169000 newtons/m² or 169000 Pascals.
That is house b. house a is unknown.
but check my arithmetic.
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