Question

A rectangular water reservoir is 5 m by 4 m at the base. Water flows into it through a pipe whose cross-section is 5 cm × 3 cm at the rate of 2/3 m/sec. Find the height to which the water will rise in the reservoir in 25 minutes.

Answer 1

Given:

Reservoir base = 5 m × 4 m.

Pipe cross-section = 5 cm × 3 cm.

Water speed in pipe = 2/3 m/s.

Time = 25 minutes.

Step-wise calculation:

1. Pipe area:

5 cm × 3 cm 

= 15 cm² 

= 15 × 10^–4 m²

= 0.0015 m²

2. Volumetric flow rate

Q = Area × Speed 

= `0.0015 xx 2/3`

= 0.001 m³/s.

3. Time in seconds

t = 25 × 60 

= 1500 s

4. Volume of water delivered

V = Q × t 

= 0.001 × 1500

= 1.5 m³

5. Reservoir base area

A = 5 × 4

= 20 m²

6. Height

h = `"V"/"A"` 

= `1.5/20`

= 0.075 m 

= 7.5 cm

The water will rise to 0.075 m (7.5 cm).