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A pipe of diameter, 2.4 CM discharge water at the rate of 2.8 m/s. Find the volume of water discard in half an hour. Give your answers in litres

To solve the problem of finding the volume of water discharged by a pipe of diameter 2.4 cm at a rate of 2.8 m/s over half an hour, we can follow these steps:

### Step 1: Calculate the cross-sectional area of the pipe.
The diameter of the pipe is given as 2.4 cm. First, we convert the diameter into meters:

\[
\text{Diameter} = 2.4 \, \text{cm} = 0.024 \, \text{m}
\]

The radius \( r \) of the pipe is half of the diameter:

\[
r = \frac{0.024 \, \text{m}}{2} = 0.012 \, \text{m}
\]

The cross-sectional area \( A \) of the pipe (which is circular) is calculated using the formula for the area of a circle:

\[
A = \pi r^2 = \pi (0.012 \, \text{m})^2 \approx 4.52 \times 10^{-4} \, \text{m}^2
\]

### Step 2: Calculate the volume flow rate.
The velocity of the water is given as 2.8 m/s. The volume flow rate \( Q \) is calculated as:

\[
Q = A \times \text{velocity} = 4.52 \times 10^{-4} \, \text{m}^2 \times 2.8 \, \text{m/s} \approx 1.2656 \times 10^{-3} \, \text{m}^3/\text{s}
\]

### Step 3: Calculate the total volume of water discharged in half an hour.
Half an hour is 1800 seconds. The total volume \( V \) discharged is:

\[
V = Q \times \text{time} = 1.2656 \times 10^{-3} \, \text{m}^3/\text{s} \times 1800 \, \text{s} \approx 2.2781 \, \text{m}^3
\]

### Step 4: Convert the volume to liters.
1 cubic meter is equivalent to 1000 liters. Thus:

\[
V = 2.2781 \, \text{m}^3 \times 1000 \, \text{L/m}^3 = 2278.1 \, \text{L}
\]

### Final Answer:
The volume of water discharged in half an hour is approximately **2278.1 liters**.

Would you like more details on any specific part of the solution or have any other questions?

Here are some related questions you might find interesting:
1. How does the diameter of the pipe affect the discharge rate?
2. What would be the volume of water discharged if the velocity were doubled?
3. How would the discharge volume change if the time were reduced to 15 minutes?
4. What formulae are used to convert cubic meters to liters?
5. How can you calculate the discharge rate if the pipe were not circular?

**Tip:** Always check the units of each quantity in a problem to ensure they are consistent, especially when converting between different systems (e.g., metric and imperial).

Learn how to calculate the volume of water discharged by a pipe with a diameter of 2.4 cm at a velocity of 2.8 m/s over half an hour. Detailed step-by-step solution included. Answer provided in liters.

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