## “a spherical water tank, 24 ft in diameter, sits atop a 60 ft tower. the tank is filled by a hose attached to the bottom of the sphere. if a

Question

“a spherical water tank, 24 ft in diameter, sits atop a 60 ft tower. the tank is filled by a hose attached to the bottom of the sphere. if a 1.5 horsepower pump is used to deliver water up to the tank”, how long will it take to fill the tank?

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3 years 2021-07-25T23:08:45+00:00 2 Answers 142 views 0

9.14hrs

Explanation:

1 horse power = 745.7 watts

1.5 horse power = 1118.55 watts

1 ft = 0.305 m

24 ft = 7.3152 m

60 ft = 18.288 m

the water tank is spherical, volume of a spherical tank = 3/4 πr³ where is r is the radius of the tank = 7.3152 m  / 2 = 3.66 m

volume = 4/3 ( 3.66 m ³) × 3.142 = 205.394 m³

mass of water = density × volume = 205.394 m³ × 1000kg/m³ = 205,394 kg

weight of water = mass × acceleration due to gravity = 205,394 kg  ×  9.8 = 2012861.2 N

potential energy stored at the height where water was  stored = mgh = weight × height  = 2012861.2 N × 18.288 m

potential energy stored = energy from the pump = power in watt × t

1118.55 watts  × t =2012861.2 N × 18.288 m

t = (2012861.2 N × 18.288 m) / 1118.55 watts = 32846.62 secs = 9.14 hrs

time taken =10.86 hrs

Explanation:

Since the tank is spherical, we will calculate the volume of a sphere

The radius of the tank, r = Diameter/2

r = 24/2 = 12 ft

Volume , V = 4/3 πr³

V = 4/3 * π * 12³

V = 7238.23 ft³

1 ft = 0.3048 m

V = 7238.23 * (0.3048)³

V = 204.96 m³

Density of water, ρ = 1000 kg/m³

Density = mass/volume

ρ = M/V

Mass, M =  ρ V

Mass = 1000 * 204.96

Mass = 204960 kg

The center of gravity of the tank is at the center of the spherical tank

Height of the center of the tank, h = 12 + 60 = 72 ft

h = 72 * 0.3048

h = 21.75 m

Workdone by the pump,W= mgh

W = 204960 * 9.81 * 21.75

W = 43731802.8 Joules

Power = Work/time

The pump capacity = 1.5 hp

1 hp = 745.7 W

1.5 hp = 1118.55 W

Pt = W

1118.55 * t = 43731802.8

t = 43731802.8/1118.55

t = 39098.62 s

t = 39098.62/3600

t = 10.86 hrs