Final answer:
The speed of water leaving the pipe is approximately 8.86 m/s.
Step-by-step explanation:
To find the speed of water leaving the pipe, we can use Bernoulli's equation. Bernoulli's equation states that the sum of the pressure, kinetic energy, and potential energy per unit volume is constant along a streamline.
At point-1, the pressure is the atmospheric pressure, the height is 10.00 m, and the cross-sectional area is 3.00 m². At point-2, the pressure is atmospheric pressure (since it is specified in the question), the height is 6.0 m, and the cross-sectional area is 1.500 m².
Using Bernoulli's equation:
P₁ + ρgh₁ + 1/2ρv₁² = P₂ + ρgh₂ + 1/2ρv₂²
Substituting the known values:
Patm + ρgh₁ + 0 = Patm + ρgh₂ + 1/2ρv₂²
Since the valve is opened wide and the water is allowed to flow freely, the velocity at point-1 (where the pipe terminates) is the speed of the water leaving the pipe.
Solving for v₂:
v₂ = √(2g(h₁ - h₂))
Substituting the values:
v₂ = √(2 * 9.8 * (10.00 - 6.00))
v₂ ≈ 8.86 m/s