A hose-pipe of cross-section area `2cm^(2)` delivers 1500 litres of water in 5 minutes. What is the speed of water in m/s through the pipe?

Answer

To find the speed of water flowing through the hose-pipe, we can follow these steps:

### Step 1: Convert the volume of water delivered to cubic centimeters per second.
The hose-pipe delivers 1500 liters of water in 5 minutes.

1 liter = 1000 cubic centimeters (cm³), so:
\[ 1500 \text{ liters} = 1500 \times 1000 \text{ cm}^3 = 1500000 \text{ cm}^3 \]

Now, we need to find the volume delivered per second:
\[ \text{Volume per second} = \frac{1500000 \text{ cm}^3}{5 \text{ minutes} \times 60 \text{ seconds/minute}} = \frac{1500000 \text{ cm}^3}{300 \text{ seconds}} = 5000 \text{ cm}^3/\text{s} \]

### Step 2: Use the formula for flow rate to find the speed of water.
The flow rate can be expressed as:
\[ \text{Volume} = \text{Area} \times \text{Speed} \]
Where:
- Volume = 5000 cm³/s (from Step 1)
- Area = 2 cm² (given in the question)
- Speed = ? (what we are trying to find)

Rearranging the formula to solve for speed:
\[ \text{Speed} = \frac{\text{Volume}}{\text{Area}} = \frac{5000 \text{ cm}^3/\text{s}}{2 \text{ cm}^2} \]

### Step 3: Calculate the speed.
\[ \text{Speed} = \frac{5000}{2} = 2500 \text{ cm/s} \]

### Step 4: Convert the speed from cm/s to m/s.
Since 1 m = 100 cm, we can convert cm/s to m/s:
\[ \text{Speed in m/s} = \frac{2500 \text{ cm/s}}{100} = 25 \text{ m/s} \]

### Final Answer:
The speed of water through the pipe is **25 m/s**.

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