Unit Conversions

Standardize units to meters for consistency.

• Water flow rate: $12 \text{ km/hr} = 12 \times \frac{1000 \text{ m}}{3600 \text{ s}} = \frac{10}{3} \text{ m/s}$
• Pipe radius ($r$): Diameter = 14 cm, so radius = 7 cm = $0.07 \text{ m}$
• Desired water level rise ($h$): 28 cm = $0.28 \text{ m}$
• Tank length ($L$): 60 m
• Tank width ($W$): 33 m

Calculate Volume Needed in Tank

Find the volume of water required to raise the level by 28 cm.

Volume ($V_{tank}$) = Tank Length $\times$ Tank Width $\times$ Height Rise

$V_{tank} = 60 \text{ m} \times 33 \text{ m} \times 0.28 \text{ m} = 554.4 \text{ m}^3$

Calculate Water Flow Rate from Pipe

Determine the volume of water passing through the pipe per second.

Cross-sectional area of the pipe ($A_{pipe}$) = $\pi r^2$

$A_{pipe} = \pi (0.07 \text{ m})^2 = 0.0049\pi \text{ m}^2$

Volume flow rate ($Q$) = Area $\times$ Velocity

$Q = 0.0049\pi \text{ m}^2 \times \frac{10}{3} \text{ m/s} = \frac{0.049\pi}{3} \text{ m}^3/\text{s}$

Determine Time to Fill Volume

Calculate the time needed by dividing the required tank volume by the flow rate.

Time ($T$) = $\frac{V_{tank}}{Q}$

$T = \frac{554.4 \text{ m}^3}{\frac{0.049\pi}{3} \text{ m}^3/\text{s}} = \frac{554.4 \times 3}{0.049\pi} \text{ s}$

Substitute $\pi \approx \frac{22}{7}$:

$T = \frac{554.4 \times 3}{0.049 \times \frac{22}{7}} \text{ s} = \frac{554.4 \times 3 \times 7}{0.049 \times 22} \text{ s} = \frac{11642.4}{1.078} \text{ s} = 10800 \text{ s}$

Convert Time to Hours

Convert the calculated time from seconds to hours.

Time in hours = $\frac{10800 \text{ s}}{3600 \text{ s/hr}} = 3 \text{ hrs}$