(a) A tank has a circular orifice 20mm diameter in the vertical side near the bottom. It contains water to a depth of Im above the orifice with oil of relative density 0.8 for a depth of Im above the water. Acting on the upper surface of the oil-is an air pressure on 20kN/m². The jet of water issuing from the orifice travels a horizontal distance of 1.5m from the orifice while falling a vertical distance of 0.156m. If the coefficient of contraction of the orifice is 0.65, estimate. find:(b) The value of the coefficient of velocity, d (ii) The actual discharge through the orifice.

To solve this problem, we need to use the principles of fluid dynamics.

Step 1: Calculate the total pressure at the orifice.

The total pressure at the orifice is the sum of the pressure due to the oil, the pressure due to the water, and the air pressure.

Pressure due to oil = height of oil * density of oil * gravity = 1m * 800kg/m³ * 9.81m/s² = 7848 Pa

Pressure due to water = height of water * density of water * gravity = 1m * 1000kg/m³ * 9.81m/s² = 9810 Pa

Air pressure = 20kN/m² = 20000 Pa

Total pressure = 7848 Pa + 9810 Pa + 20000 Pa = 37658 Pa

Step 2: Calculate the theoretical velocity of the jet at the orifice.

The theoretical velocity can be calculated using Torricelli's theorem, which states that the velocity of a jet of fluid exiting an orifice under the force of gravity alone is v = sqrt(2gh), where g is the acceleration due to gravity and h is the height of the fluid above the orifice.

In this case, the height is the total pressure divided by the density of water and gravity, h = P/(ρg) = 37658 Pa / (1000kg/m³ * 9.81m/s²) = 3.84m

So, the theoretical velocity v = sqrt(2 * 9.81m/s² * 3.84m) = 8.72 m/s

Step 3: Calculate the coefficient of velocity.

The coefficient of velocity is the ratio of the actual velocity to the theoretical velocity. The actual velocity can be calculated from the horizontal and vertical distances the jet travels, v = sqrt((x²g)/2y), where x is the horizontal distance and y is the vertical distance.

In this case, v = sqrt((1.5m² * 9.81m/s²) / (2 * 0.156m)) = 7.24 m/s

So, the coefficient of velocity = actual velocity / theoretical velocity = 7.24 m/s / 8.72 m/s = 0.83

Step 4: Calculate the actual discharge through the orifice.

The actual discharge is the product of the area of the orifice, the actual velocity, and the coefficient of contraction.

The area of the orifice is πd²/4 = π * (0.02m)² / 4 = 0.000314 m²

So, the actual discharge Q = area * velocity * coefficient of contraction = 0.000314 m² * 7.24 m/s * 0.65 = 0.00148 m³/s or 1.48 litres/s.