Water running in a cylindrical pipe of inner diameter 7 cm, is collected in a container at the rate of 192.5 litres per minute. Find the rate of flow of water in the pipe in km/hr.

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Convert the flow rate from liters to cubic centimeters.
1 liter is equal to 1000 cubic centimeters (cm³). Therefore, the flow rate of water collected in the container is:
\[ 192.5 \text{ liters/minute} = 192.5 \times 1000 \text{ cm}^3/\text{minute} = 192500 \text{ cm}^3/\text{minute} \]

### Step 2: Find the radius of the cylindrical pipe.
The inner diameter of the pipe is given as 7 cm. The radius (r) can be calculated as:
\[ r = \frac{\text{diameter}}{2} = \frac{7 \text{ cm}}{2} = 3.5 \text{ cm} \]

### Step 3: Calculate the cross-sectional area of the pipe.
The cross-sectional area (A) of the cylindrical pipe can be calculated using the formula for the area of a circle:
\[ A = \pi r^2 = \frac{22}{7} \times (3.5)^2 \]
Calculating \( (3.5)^2 \):
\[ (3.5)^2 = 12.25 \]
Now substituting back:
\[ A = \frac{22}{7} \times 12.25 = \frac{22 \times 12.25}{7} = \frac{269.5}{7} \approx 38.5 \text{ cm}^2 \]

### Step 4: Relate the volume flow rate to the height of water in the pipe.
The volume of water flowing through the pipe in one minute is equal to the cross-sectional area multiplied by the height (h) of water that flows in that time:
\[ \text{Volume} = \text{Area} \times \text{Height} \Rightarrow 192500 \text{ cm}^3 = 38.5 \text{ cm}^2 \times h \]
To find h:
\[ h = \frac{192500}{38.5} \approx 5000 \text{ cm} \]

### Step 5: Convert height to meters.
Since 100 cm = 1 m, we convert:
\[ 5000 \text{ cm} = \frac{5000}{100} = 50 \text{ m} \]

### Step 6: Calculate the rate of flow in meters per minute.
The height of water flowing in one minute is 50 m, so the rate of flow is:
\[ \text{Rate} = 50 \text{ m/min} \]

### Step 7: Convert the rate from meters per minute to kilometers per hour.
To convert meters per minute to kilometers per hour, we multiply by 60 (to convert minutes to hours) and divide by 1000 (to convert meters to kilometers):
\[ \text{Rate in km/hr} = 50 \times 60 \div 1000 = 3 \text{ km/hr} \]

### Final Answer:
The rate of flow of water in the pipe is **3 km/hr**.

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