Water is being poured in a vessel at a constant rate α m3 s- 1 . There is a small hole of the area a at the bottom of the tank. The maximum level of water in the vessel is

Question

Water is being poured in a vessel at a constant rate α m3 s- 1 . There is a small hole of the area a at the bottom of the tank. The maximum level of water in the vessel is (A) h=(α 2/2 g a2) (B) h=(α 2/4 g a2) (C) h=(α 2/ g a2) (D) h=(3 α 2/g a2)

Tardigrade Admin · Accepted Answer

Level of water in the vessel will be maximum when

r a t e o f in f l o w o f w a t er = r a t e o f o u t f l o w o f w a t er

.
or

α = a v

or

α = a 2 g h

or

h = \frac{α ^{2}}{2 g a ^{2}}

Q. Water is being poured in a vessel at a constant rate $α m^{3} s^{- 1}$ . There is a small hole of the area $a$ at the bottom of the tank. The maximum level of water in the vessel is

$h = \frac{α ^{2}}{2 g a ^{2}}$

$h = \frac{α ^{2}}{4 g a ^{2}}$

$h = \frac{α ^{2}}{g a ^{2}}$

$h = \frac{3 α ^{2}}{g a ^{2}}$

Level of water in the vessel will be maximum when $r a t e o f in f l o w o f w a t er = r a t e o f o u t f l o w o f w a t er$ .
or $α = a v$

or $α = a 2 g h$
or $h = \frac{α ^{2}}{2 g a ^{2}}$

Q. Water is being poured in a vessel at a constant rate αm3s−1 . There is a small hole of the area a at the bottom of the tank. The maximum level of water in the vessel is

h=2ga2α2​

h=4ga2α2​

h=ga2α2​

h=ga23α2​