The drawing shows a spherical reservoir that contains 7.05x10^5 kg of water when

Question

The drawing shows a spherical reservoir that contains 7.05x10^5 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) in House B. Ignore the diameter of the delivery of pipes.

The length of the water tower is 15.0m above the ground to the point where the water is all held (15.0m from ground to the bottomr of bulb). the distance that House B is above ground level 7.30m. House A is at ground level.

Explanation / Answer

Given that

The mass of water contained in the reservoir (m) = 7.05x10^5 kg

The volume of the sphere is given by (V) =(4/3)pir3

We also know that density =mass/volume then v =m/p

m/p =(4/3)pir3

then r =(3m/4pip)1/3 =(0.75*m/p*pi)1/3 =(0.75*7.05x10^5/1000*3.14)1/3 =5.522m

Now the gauge pressure that the water has at the faucet in (a) House A is

hA =2r+H =2(5.522)+H then H =15m is given

Now the pressure at point A is PA =hA *p*g =

And the pressure at point B is PB =(hA-H)*p*g

where p =1000kg/m3 and g =9.81m/s2

substitute the values to get the required answers

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