Question

An 800-gallon, 1.2 m wide cylindrical water tank is filled to the brim. The tank has a hole
formed at 13.3 cm above the ground. It is observed that water leaks out of the reservoir at a
speed that reduces by 3.2 m.s-1
in 1 minute 39 seconds. If the tank was initially filled to the
brim

how much water leaked out of the tank, and
8.2 by how much shall the point, at which water lands, change?
(1 gallon = 4.55 l)

Answer 1

1) how much water leaked out ?

given that the velocity is reduced by 3.2 m/s i99 seconds

we know from torcelli's equation that

V_f =

where Vf is the flow velocity and h is the heught of the liquid column above

initially the height of liquid column above the hole = 120 cm -13.3 cm = 106.7 cm

now change in velocity =3.2

subsituting the respective values we get H_f = 9.619 cm

i.e the toatal level of water from ground = 22.91 cm

we know that the volume of water is directly proportional to height of water level from ground

so we get the remaining volume as 695.21 l= 152.79 gallons

2) we know from kinematics that the range of an object thrown from height h depends on velocity as

now difference in range =

since the height i ssam e i.e 13.3 cm and difference of velocity = 3.2

so we get the change in point where water lands as 0.368 m =36.85 cm

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Peace

-V.K