Water is flowing at the rate of 6km/hr through a pipe of diameter 14 cm into a rectangular tank which is 60 m long and 22 m wide. Determine the time in which the level of water in the tank will rise by 7 cm.

Answer

To solve the problem step by step, we need to find the time it takes for the water level in the rectangular tank to rise by 7 cm when water is flowing through a pipe.

### Step 1: Convert the given dimensions and flow rate into consistent units.
- The diameter of the pipe is given as 14 cm, which can be converted to meters:
\[ \text{Diameter} = 14 \text{ cm} = 0.14 \text{ m} \]
- The flow rate of water is given as 6 km/hr, which can be converted to meters per second:
\[ 6 \text{ km/hr} = \frac{6 \times 1000 \text{ m}}{3600 \text{ s}} = \frac{6000}{3600} = \frac{5}{3} \text{ m/s} \]

### Step 2: Calculate the volume of water that needs to be added to the tank.
- The dimensions of the rectangular tank are:
- Length (L) = 60 m
- Width (B) = 22 m
- Height increase (H) = 7 cm = 0.07 m
- The volume (V) of water needed to raise the water level by 7 cm in the tank is given by:
\[ V = L \times B \times H = 60 \text{ m} \times 22 \text{ m} \times 0.07 \text{ m} = 92.4 \text{ m}^3 \]

### Step 3: Calculate the cross-sectional area of the pipe.
- The radius (r) of the pipe is:
\[ r = \frac{\text{Diameter}}{2} = \frac{0.14 \text{ m}}{2} = 0.07 \text{ m} \]
- The cross-sectional area (A) of the pipe is given by:
\[ A = \pi r^2 = \pi (0.07 \text{ m})^2 \approx 0.0154 \text{ m}^2 \]

### Step 4: Calculate the volume of water flowing through the pipe per second.
- The volume flow rate (Q) can be calculated as:
\[ Q = A \times \text{Flow Rate} = 0.0154 \text{ m}^2 \times \frac{5}{3} \text{ m/s} \approx 0.0257 \text{ m}^3/\text{s} \]

### Step 5: Calculate the time required to fill the tank.
- The time (t) required to fill the volume of water needed can be calculated using:
\[ t = \frac{V}{Q} = \frac{92.4 \text{ m}^3}{0.0257 \text{ m}^3/\text{s}} \approx 3600 \text{ s} \]
- Converting seconds to hours:
\[ t = \frac{3600 \text{ s}}{3600 \text{ s/hr}} = 1 \text{ hour} \]

### Final Answer:
The time in which the level of water in the tank will rise by 7 cm is **1 hour**.

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