Question

A cylindrical pipe of radius $1.4\,\text{m}$ has water flowing out at $2.5\,\text{m/s}$ into a cuboidal tank of dimensions $28\,\text{m}\times 11\,\text{m}\times 25\,\text{m}$. The flow completely occupies the pipe's cross-section. What percentage of the tank is filled up in $8$ min $20$ s?

• A. 66.66%
• B. 100%
• C. 86%
• D. 75%

Hint:

For steady flow, use $Q=Av$ and $V=Qt$. Converting time to seconds keeps units consistent; then compare $V$ to the tank capacity for the percentage.

Answer 1

The Correct Option is B

Step 1: Pipe cross-section with \(\pi=\tfrac{22}{7}\): \( A=\tfrac{22}{7}\times1.4^2=6.16\ \text{m}^2 \).

Step 2: Flow rate \(=6.16\times2.5=15.4\ \text{m}^3/\text{s}\); over \(t=500\,\text{s}\), volume in \(=15.4\times500=7700\ \text{m}^3\).

Step 3: Tank volume \(=28\times11\times25=7700\ \text{m}^3\), so the fill percentage is \(\tfrac{7700}{7700}\times100=100\%\). \[ \boxed{100\%} \]