To calculate the speed of water flowing in a pipe, you can use the principle of volumetric flow rate. The volumetric flow rate ([tex]\( Q \)[/tex]) is given by the formula:
[tex]\[ Q = \text{Volume} (V) / \text{Time} (t) \][/tex]
Additionally, the volumetric flow rate ([tex]\( Q \)[/tex]) is also related to the cross-sectional area ([tex]\( A \)[/tex]) of the pipe and the velocity ([tex]\( v \)[/tex]) of the fluid flowing through it:
[tex]\[ Q = A \cdot v \][/tex]
Therefore, to find the velocity ([tex]\( v \)[/tex]), we can rearrange this formula:
[tex]\[ v = \frac{Q}{A} \][/tex]
Let's break down the problem step by step:
1. Convert the volume of water from liters to cubic centimeters:
Given:
- Volume ([tex]\( V \)[/tex]) = 3.0 liters
- Time ([tex]\( t \)[/tex]) = 20 seconds
Since 1 liter = 1000 cubic centimeters (cm³), we have:
[tex]\[ V = 3.0 \text{ liters} \times 1000 \text{ cm}³/\text{liter} = 3000 \text{ cm}³ \][/tex]
2. Calculate the volumetric flow rate ([tex]\( Q \)[/tex]):
[tex]\[ Q = \frac{V}{t} = \frac{3000 \text{ cm}³}{20 \text{ s}} = 150 \text{ cm}³/\text{s} \][/tex]
3. Calculate the cross-sectional area of the pipe:
Given:
- Cross-sectional area ([tex]\( A \)[/tex]) = 4.0 cm²
4. Determine the velocity ([tex]\( v \)[/tex]) of the water:
[tex]\[ v = \frac{Q}{A} = \frac{150 \text{ cm}³/\text{s}}{4.0 \text{ cm}²} = 37.5 \text{ cm/s} \][/tex]
5. Convert the velocity from cm/s to m/s:
Since 1 cm = 0.01 m, we have:
[tex]\[ v = 37.5 \text{ cm/s} \times 0.01 \text{ m/cm} = 0.375 \text{ m/s} \][/tex]
So, the speed of water flowing in the pipe is [tex]\(0.375 \text{ m/s}\)[/tex].
Therefore, the correct answer is:
O 0.375 m/s
