Respuesta :
Answer:
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
Answer:
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
