To solve the problem step by step, we will determine how long it takes for the water level in the tank to reach 8 meters given the dimensions of the tank and the flow rate of the water through the pipe.
### Step 1: Calculate the volume of water needed to fill the tank to 8 meters.
The formula for the volume \( V \) of a rectangular tank is:
\[
V = \text{length} \times \text{width} \times \text{height}
\]
Given:
- Length of the tank = 200 m
- Width of the tank = 150 m
- Height of water to be filled = 8 m
Substituting the values:
\[
V = 200 \, \text{m} \times 150 \, \text{m} \times 8 \, \text{m} = 240000 \, \text{m}^3
\]
### Step 2: Calculate the flow rate of water through the pipe.
The cross-sectional area \( A \) of the pipe is given by:
\[
A = \text{width} \times \text{height}
\]
Given:
- Width of the pipe = 0.3 m
- Height of the pipe = 0.2 m
Calculating the area:
\[
A = 0.3 \, \text{m} \times 0.2 \, \text{m} = 0.06 \, \text{m}^2
\]
Next, we need to find the volume of water flowing through the pipe in one hour. The speed of water flow is given as 20 km/h, which we convert to meters per second:
\[
20 \, \text{km/h} = \frac{20 \times 1000 \, \text{m}}{3600 \, \text{s}} \approx 5.56 \, \text{m/s}
\]
Now, we can calculate the volume of water flowing through the pipe in one hour (3600 seconds):
\[
\text{Volume in one hour} = A \times \text{speed} \times \text{time} = 0.06 \, \text{m}^2 \times 5.56 \, \text{m/s} \times 3600 \, \text{s}
\]
Calculating:
\[
\text{Volume in one hour} = 0.06 \times 5.56 \times 3600 \approx 120.192 \, \text{m}^3
\]
### Step 3: Calculate the time required to fill the tank.
To find the time \( t \) required to fill the tank to a height of 8 meters, we use the formula:
\[
t = \frac{\text{Volume of water needed}}{\text{Volume of water supplied in one hour}}
\]
Substituting the values:
\[
t = \frac{240000 \, \text{m}^3}{120.192 \, \text{m}^3} \approx 1998.4 \, \text{hours}
\]
### Conclusion
The time required for the water level in the tank to reach 8 meters is approximately **2000 hours**.
