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

Answers ( )

  1. thnahdat
    0
    2021-07-25T23:09:51+00:00
    Reply

    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

  2. ngocdiep
    0
    2021-07-25T23:10:21+00:00
    Reply

    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

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