Question

A cylindrical water tank of diameter 14m is filled by water flowing from a pipe of radius 70mm at the rate of 7m/s. If the height of the tank is 7m. Take 22/7. How long does it take to fill the tank completely(in hours). Please explain in asimple way please

Answer 1

To find out how long it takes to fill the cylindrical water tank, we need to follow these steps:

1. **Calculate the volume of the tank**:
The formula for the volume of a cylinder is:
\[
\text{Volume} = \pi r^2 h
\]
where \( r \) is the radius and \( h \) is the height.

- The diameter of the tank is 14 m, so the radius \( r \) is half of the diameter:
\[
r = \frac{14}{2} = 7 \text{ m}
\]
- The height \( h \) of the tank is given as 7 m.
- Using \( \pi \) as \( \frac{22}{7} \):
\[
\text{Volume of the tank} = \frac{22}{7} \times (7)^2 \times (7)
\]
\[
= \frac{22}{7} \times 49 \times 7
\]
\[
= \frac{22 \times 49 \times 7}{7}
\]
\[
= 22 \times 49
\]
\[
= 1078 \text{ m}^3
\]

2. **Calculate the flow rate from the pipe**:
The flow rate can be calculated using the area of the pipe and the velocity of water.

- The radius of the pipe is given as 70 mm, which we convert to meters:
\[
r_{\text{pipe}} = 70 \text{ mm} = 0.07 \text{ m}
\]
- The cross-sectional area \( A \) of the pipe is given by:
\[
A = \pi r_{\text{pipe}}^2
\]
\[
= \frac{22}{7} \times (0.07)^2
\]
\[
= \frac{22}{7} \times 0.0049
\]
\[
= \frac{22 \times 0.0049}{7}
\]
\[
= \frac{0.1078}{7}
\]
\[
\approx 0.0154 \text{ m}^2
\]
- The flow rate \( Q \) is given by:
\[
Q = \text{Area} \times \text{velocity}
\]
\[
= 0.0154 \text{ m}^2 \times 7 \text{ m/s}
\]
\[
= 0.1078 \text{ m}^3/\text{s}
\]

3. **Calculate the time to fill the tank**:
To find the time \( t \) required to fill the tank, use:
\[
t = \frac{\text{Volume}}{\text{Flow Rate}}
\]
\[
= \frac{1078 \text{ m}^3}{0.1078 \text{ m}^3/\text{s}}
\]
\[
\approx 9995.16 \text{ seconds}
\]

4. **Convert seconds to hours**:
To convert seconds into hours, divide by the number of seconds in an hour (3600 seconds):
\[
\text{Time in hours} = \frac{9995.16 \text{ seconds}}{3600 \text{ seconds/hour}}
\]
\[
\approx 2.77 \text{ hours}
\]

Therefore, it takes approximately **2.77 hours** to fill the tank completely.