Question

Water in a rectangular reservoir having base 80 m by 60 m is 6.5 m deep. In what time can the water be emptied by a pipe of which the cross-section is a square of side 20 cm, if the water runs through the pipe at the rate of 15 km/hr.

Answer 1

Time can the water be emptied by a pipe is 52 hours

Step-by-step explanation:

• Given data about reservoir

        Length of reservoir (L) = 60 m

        Breadth of reservoir (B) = 60 m

        Height of reservoir (H) = 6.5 m

        From formula

        Volume of reservoir = Length ×Breadth ×Height

        Volume of reservoir = 80 ×60 ×6.5

• Given data about pipe

        Cross-sectional shape of pipe is a square.

        Side of square (a) = 20 cm = 0.2 m

        Cross- sectional area of pipe = Side ×Side =0.2×0.2=0.04

• Speed of water $\mathbf{=15 \ \frac{km}{h}=15\times \frac{5}{18} = \frac{25}{6} \ \frac{m}{s}}$

        Let time taken to empty reservoir = t   sec

        So distance travel by water in t sec

        Distance =Speed ×Time$\mathbf{=\frac{25}{6}\times t=\frac{25t}{6} \ m}$

Volume travel by water through pipe = Cross-sectional area×Distance

        So

        Volume travel by water through pipe$\mathbf{=\frac{0.04\times 25t}{6} \ m^{3}}$

• Now

        Volume travel by water through pipe= Volume of reservoir

         $\mathbf{\frac{0.04\times 25t}{6}=80\times 60\times 6.5}$

         On solving above, we get

        t = 187200 sec = 52 hours