A cylinderical tank of height 0.4 m is open at the top and has a diameter 0.16m. Water is filled in it up to height of 0.16 m. Find the time taken to empty the tank through a hole of radius `5 xx 10^(-3)m` in its bottom.
Text Solution
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The velocity of efflux through a small hole at a depth h is given by ` v = sqrt(2gh)` According to the principle of continuity we get ` - piR^(2) (dh)/(dt) = pir^(2) v` Since the rate of fall of water level in the tank is ` - (dh//dt)` `rArr - R^(2) (dh)/(dt) = r^(2) sqrt(2gh)` ` rArr - (dh)/(sqrt(h)) = (r^(2))/(R^(2)) sqrt(2g) .dt` Integrating we get ` - int _(0.16)^(0) (dh)/(sqrt(h)) = ((0.005)/(0.08))^(2) sqrt(2 xx 9.8 ) int_(0)^(t) dt ` Therefore , `t = 46.26 ` sec
A cylindrical tank of height H is open at the top end and it has a radius r . Water is filled in it up to a height of h . The time taken to empty the tank through a hole of radius r' in its bottom is
A cylindrical tank of height 2 m is open at the top and has a radius 50 cm. Water is filled in it upto a height 1.75 m. Calculate how long it will take to empty the tank through a hole of radius 0.05 cm in its bottom.
A right elliptical cylinder full of petrol has its widest elliptical side 2.4 m and the shortest 1.6 m. Its height is 7 m. Find the time required to empty half the tank through a hole of diameter 4 cm if the rate of flow of petrol is 120 m/min
A cylindrical tank has a capacity of 5632m^(3) . If the diameter of its base is 16 m, find its depth.
A cylindrical tank has a radius of 154 cm. It is filled with water to a height of 3 m. If water to a height of 4.5 m is poured into it, what will be the increase in the volume of water in kl?
A cylindrical vessel of height 500mm has an orifice (small hole) at its bottom. The orifice is initially closed and water is filled in it up to height H. Now the top is completely sealed with a cap and the orifice at the bottom is opened. Some water comes out from the orifice and the water level in the vessel becomes steady with height of water column being 200mm. Find the fall in height(in mm) of water level due to opening of the orifice. [Take atmospheric pressure =1.0xx10^5N//m^2 , density of water=1000kg//m^3 and g=10m//s^2 . Neglect any effect of surface tension.]
Dimensions of cylindrical overhead tank are, radius = 6m and height = 7m. If water is filled in at the rate of 20 litre per minute, the tank will be completely filled in how much time?
FIITJEE-FLUID MECHANICS -ASSIGHNMENT COMPREHENSION NUMERICAL BASED QUESTIONS
