Answer:
0.0000333 m³/s
Explanation:
using Bernoulli's equation
P1 + 1/2ρv1² + ρh1g = P2 + 1/2ρv2² + ρh2g
P1 = P2 both are atmospheric pressure; they cancel out
1/2ρv1² + ρh1g = 1/2ρv2² + ρh2g divide both side with ρ (rho)
1/2v1² + h1g = 1/2v2² +h2g
collect the like terms
h1g - h2g = 1/2v2² + 1/2v1²
multiply both side by 2 and take g out from the left equation
2g(h1 - h2) = v2² + v1² where v1 is approximately 0 assuming the surface of the tank is large
v2² = 2g(h1 - h2)
take square root of both sides
v2 = √2g(h1 - h2)
h1 = 3.75 + 6.5 = 10.25
h2 = 6.5
v2 = √2g(h1 - h2) = √ (2×9.81× (10.25 - 6.5)) = 8.6 m/s
Volume in m³/s = A × v where A is the area of the hole and the radius of the hole = 2.22 mm / 2 (where 2.22 mm is the diameter of the hole) = 1.11 mm and 1.11mm / 1000 to convert it to meters
Area of the hole ( assuming it is a circle) = πr² = 3.142× (1.11/1000)²
Area = 0.00000387 m²
Volume in M³/s = 0.00000387 × 8.6 = 0.0000333 m³/s
