Answer:
Speed of Water = 2.652 ms⁻¹
Explanation:
Step 1: Calculate the Radius of the Faucet:
Radius = Diameter / 2
Radius = 2 cm / 2
Radius = 1 cm or 0.01 m
Step 2: Calculate Cross-Section Area of Faucet:
Area = π r²
Area = π (0.01 m)²
Step 3: Calculate the Flow Rate (Q) as;
Q = 2.5 × 10⁻² m³ / 30 s
Q = 8.33 × 10⁻⁴ m³/s
Step 4: Calculate Speed of water as;
Speed of Water = Flow Rate / Cross-Section Area
Putting values,
Speed of Water = 8.33 × 10⁻⁴ m³/s / π (0.01 m)²
Speed of Water = 8.33 × 10⁻⁴ m³/s / 3.14 × 0.0001 m²
Speed of Water = 8.33 × 10⁻⁴ m/s / 0.000314
Speed of Water = 2.652 ms⁻¹
Given values:
The radius of Faucet will be:
→ [tex]Radius = \frac{Diameter}{2}[/tex]
[tex]= \frac{2}{2}[/tex]
[tex]= 1 \ cm \ or \ 0.01 \ m[/tex]
The Cross-section area of Faucet will be:
→ [tex]Area = \pi r^2[/tex]
[tex]= \pi (0.01)^2[/tex]
The flow rate will be:
→ [tex]Q = \frac{2.5\times 10^{-2}}{30}[/tex]
[tex]= 8.33\times 10^{-4} \ m^3/s[/tex]
hence,
The speed of water will be:
= [tex]\frac{Flow \ rate}{Cross-section \ area}[/tex]
= [tex]\frac{8.33\times 10^{-4}}{\pi (0.01)^2}[/tex]
= [tex]\frac{8.33\times 10^{-4}}{0.000314}[/tex]
= [tex]2.652 \ ms^{-1}[/tex]
Thus the above approach is right.
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