A tank is 7 metre long and 4 metre wide. At what speed should water run through a pipe 5 cm broad and 4 cm deep so that in 6 hours and 18 minutes water level in the tank rise by 4.5 metre?

### Concept & Formula The volume of water that flows through the pipe in a given time must equal the volume of water accumulated in the tank. The flow volume is the cross-sectional area of the pipe multiplied by the water speed and the time elapsed. $$\text{Volume of Tank} = L \times W \times H$$ $$\text{Flow Volume} = \text{Area of Pipe} \times \text{Speed} \times \text{Time}$$ ### Step-by-Step Solution 1. **Calculate Target Volume:** $$\text{Volume} = 7 \text{ m (length)} \times 4 \text{ m (width)} \times 4.5 \text{ m (rise in level)}$$ $$\text{Volume} = 126 \text{ m}^3$$ 2. **Convert Pipe Dimensions:** Width = $5 \text{ cm} = 0.05 \text{ m}$ Depth = $4 \text{ cm} = 0.04 \text{ m}$ $$\text{Area of Pipe} = 0.05 \times 0.04 = 0.002 \text{ m}^2$$ 3. **Convert Time:** $$6 \text{ hours and } 18 \text{ minutes} = 6 + \frac{18}{60} \text{ hours} = 6 + 0.3 = 6.3 \text{ hours}$$ 4. **Set up Equation:** Let the speed be $v$ km/hr. Since dimensions are in meters, convert speed to meters/hour ($1000v$ m/hr). $$\text{Area} \times \text{Speed} \times \text{Time} = \text{Volume}$$ $$0.002 \times (1000v) \times 6.3 = 126$$ $$2v \times 6.3 = 126$$ $$12.6v = 126$$ $$v = 10 \text{ km/hr}$$ ### Exam Strategy & Shortcut Instead of converting $v$ to meters initially, calculate the speed required in meters per hour and convert to km/hr at the end. Speed (m/hr) = Volume / (Area $\times$ Time) $= 126 / (0.002 \times 6.3) = 126 / 0.0126 = 10000$ m/hr. $10000 \text{ m/hr} = 10 \text{ km/hr}$. ### Common Pitfall Failing to maintain consistent units across all measurements. Mixing cm for pipe dimensions and meters for the tank without conversion will yield a massive calculation error. ### Final Answer Therefore, the correct answer is **10 km/hr.**