A cylindrical vessel is filled with water upto a height of 1m. The cross-sectional area of the orifice at the bottom is `(1//400)` that of the vessel.
(a) What is the time required to empty the tank through the orifice at the bottom?
(b) What is the time required for the same amount of water to flow out if the water level in tank is maintained always at a height of 1m from orifice?

Options

A. `180s , 90s`
B. `90s , 180s`
C. `200s, 150s`
D. `150s , 200s`

Answer

A, B, C

Explanation

(a) Time taken to empty the tank (has been derived in theory) is
`t=(2A)/(asqrt(2g))sqrt(H)`
Given, `A/a=400`
Substituting the value we have,
`t=(2xx400)/(sqrt(2xx9.8))sqrt(1)`
`=180s=3 min`
(b) Rate of flow of water `Q=a sqrt(2gH)=constant`
Total volume of water `V=AH`
`:.` Time take to empty the tank with constant rate
`t=V/Q=(AH)/(a sqrt(2gH))`
`(400xx1)/(sqrt(2xx9.8xx1))`
`=90s =1.5 min`