To calculate the flow of water $Q$ through the drain in litres per second, we use the formula:

$Q = A \times V$

Where:

• $A$ is the cross-sectional area of the pipe in $\text{m}^2$,
• $V$ is the velocity of the water in $\text{m/s}$.

Step 1: Calculate the area of the pipe

The pipe is circular, so the area can be calculated as: $A = \pi r^2$ The diameter of the pipe is $100 \, \text{mm}$, so the radius is: $r = \frac{100}{2} = 50 \, \text{mm} = 0.05 \, \text{m}$ $A = \pi (0.05)^2$ $A \approx 3.1416 \times 0.0025 = 0.007854 \, \text{m}^2$

Step 2: Use the formula for $Q$

The velocity of the water is given as $0.6 \, \text{m/s}$: $Q = A \times V$ $Q = 0.007854 \times 0.6$ $Q = 0.0047124 \, \text{m}^3/\text{s}$

Step 3: Convert to litres per second

Since $1 \, \text{m}^3 = 1000 \, \text{litres}$: $Q = 0.0047124 \times 1000$ $Q \approx 4.712 \, \text{L/s}$

Final Answer:

The flow rate is approximately 4.71 litres per second.

Would you like further clarification or have any additional questions?

Related Questions:

1. How is the velocity of water in a pipe determined practically?
2. What is the significance of converting flow rate to litres per second?
3. How would the result change if the pipe diameter were doubled?
4. What happens to the flow rate if the velocity of water increases by 50%?
5. How does pipe roughness affect the velocity of water in the drain?

Tip:

Always ensure that units are consistent when performing calculations, particularly in metric systems, to avoid errors.