Question

A cylindrical tank of diameter 2m and height 4m is full of water.Calculate the work done in pumping the water to a height 6m above the tank

Answer 1

Answer:

3hr 12min

Let us convert every measurements into m

Diameter of the cylindrical tank =4m

Radius of the cylindrical tank =

2

4

=2 m

Height of the tank =10 m

Diameter of the cylindrical pipe =10cm

Radius of the cylindrical pipe =

2

10

=5cm

1m=100cm

5cm=

100

5

m

speed of water =2.5 km/hr

We know that 1000m=1 km

=2.5×1000m\hr

=2500 m/hr

Volume of water discharged from the cylindrical pipe =

2

1

× Volume of cylindrical tank

Area of cross section ×time×speed=

2

1

πr

2

h

πr

2

×time×speed=

2

1

πr

2

h

(

100

5

)

2

× Time ×2500=

2

1

×2

2

×10

100

5

×

100

5

× Time×2500=

2

1

×4×10

Time =2×10×

5

100

×

5

100

×

2500

1

Time=

25

80

on evaluation

=3.2 hour

We know that 1 hour=60 minute

192 minute=180+12

=3 hour and 12 minute

∴ time taken to empty the half of the tank is 3 hour and 12 minute