Question

Water is flowing at the rate of 5km/hr through a pipe of diameter 14 cm into a rectangular tank of dimensions 50m*44m . find the time in which the level of water in the tank will rise by 21cm

Answer 1

the time in which the level of water in the tank will rise by 21cm is 6 hours .

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Answer 2

QUESTION

Water is flowing at the rate of 5km/hr through a pipe of diameter 14 cm into a rectangular tank of dimensions 50m*44m . find the time in which the level of water in the tank will rise by 21cm.

Answer

Given,Speed of flow of water = 5km/hr.

         Diameter of pipe = 14cm.

         Hence,radius of pipe will be (14/2 )cm = 7cm= 0.07m.

         Dimensions of rectangular tank = 50m by 44m.                                                                    

Now,Let the level of water raises 21cm in x hours.

0r

The level of water raises 0.21m in x hours.(height of the rectangular tank)

Since the flow of water is 5km per hour.

So, Length of water column in x hours = 5×1000×(x) = 5000x m.

Since,the water is in form is inside a  cylindrical pipe,hence it will be in form of the cylinder also.

Hence,

Volume of water flowing through the cylindrical pipe in x hours

=>$\pi r^{2}$

= >22/7 × (0.07)² × 5000x

=>77x m³

But,volume of water that falls into the tank in x hours=>

length × breadth × height

=>50 × 44 × 0.21

=>462 m³

So, we get =>>>

Volume of water flowing out the pipe in x hours = volume of water in the rectangular tank in x hours

=>462m³ = 77x m³

                                                => x = 6

Hence,rise in level of water in rectangular tank by 21 cm or 0.21 m is in 6 hours.

thanks