Answer:
New speed of water is 2.8 m/s.
Explanation:
It is given that,
Speed of water, v₁ = 2.3 m/s
Diameter of pipe, d₁ = 3.2 cm
Radius of pipe, r₁ = 1.6 cm = 0.016 m
Area of pipe, [tex]A_1=\pi(0.016)^2=0.000804\ m^2[/tex]
If the pipe narrows its diameter, d₂ = 2.9 cm
Radius, r₂ = 0.0145 m
Area of pipe, [tex]A_2=\pi(0.0145)^2=0.00066\ m^2[/tex]
We need to find the new speed of the water. It can be calculated using equation of continuity as :
[tex]v_1A_1=v_2A_2[/tex]
[tex]v_2=\dfrac{v_1A_1}{A_2}[/tex]
[tex]v_2=\dfrac{2.3\ m\times 0.000804\ m^2}{0.00066\ m^2}[/tex]
[tex]v_2=2.8\ m/s[/tex]
So, the new speed of the water is 2.8 m/s. Hence, this is the required solution.
