Answer:
4.68×10⁻⁴ m³/s
Explanation:
Using Bernoulli's equation, we can relate the initial and final pressures, velocities, and elevations of the water stream. Volumetric flow rate equals velocity times cross sectional area.
(a) Bernoulli's equation is:
P₁ + ½ ρ v₁² + ρgh₁ = P₂ + ½ ρ v₂² + ρgh₂
where P is pressure, ρ is density, v is speed, g is gravity, and h is height.
Take position 1 to be the top of the tank, and position 2 to be the exit at the hole.
The top of the tank is open to air, and the water exits at atmospheric pressure, so P₁ = P₂ = 0.
The speed of the water at the top of the tank is negligible, so v₁ = 0.
Using the height of the hole as reference, h₂ = 0.
The equation simplifies to:
ρgh₁ = ½ ρ v₂²
v₂² = 2gh₁
Plugging in values:
v₂² = 2 (9.8) (14.0)
v₂ = 16.6 m/s
(b) Volumetric flow rate is equal to the velocity times cross sectional area.
Q = vA
Q = (16.6 m/s) (¼ π (0.006 m)²)
Q = 0.000468 m³/s
Q = 4.68×10⁻⁴ m³/s