Question

A raised water tank has a leak at the bottom which causes the water surface to drop from elevation 4.88m to elevation 4.57 m in a period of 12 hours. (a) What will be the elevation of the water surface in the tank after 5 full days (starting from elevation 4.88m) if no water other than the leaking water is either added or drained from the tank? The bottom of the tank is at elevation zero. (b) How long will it take to empty the tank due to leakage? (c) How long will it take to lower the water in the tank by 1.2m

Answer 1

Initial elevation of top surface of water = 4.88 m

Elevation of top surface after 12 hrs = 4.57 m

Rate of decrease in elevation per 12 hr = 0.31 m

a)

Elevation after 5 full days

Total hours = 5 * 24

= 120 hrs

Decrease in elevation after 5 days = 0.31 * 120/12

= 3.1 m

Surface elevation after 5 days = 4.88 - 3.1 = 1.78 m

b)

Time taken to empty the tank

Time required for 1 m decrease in elevation = 12/0.31 hrs

Time required to empty the tank = 4.88*12/0.31

= 188.9 hrs or 7 days and 20.9 hrs

c)

Time required to decrease elevation by 1.2 m

Time required for 1 m decrease in elevation = 12/0.31 hrs

Time required for 1.2 m decrease in elevation = 1.2 * 12/ 0.31

=46.45 hrs