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Answer :
To determine the discharge through the orifice, calculate the pressure at the upstream and downstream sides. Use the given coefficients of discharge to calculate the discharge using the formula Q = Cd * A * √(2gΔh).
To determine the discharge through the orifice, we can use the Bernoulli's equation which states that the sum of pressure energy, kinetic energy, and potential energy is constant.
Here, we can ignore the kinetic and potential energy terms since the fluid is stationary.
Therefore, the pressure at the upstream side is equal to the pressure at the downstream side.
We can calculate the pressure at the upstream side using the formula:
P = ρgh.
ρ is the density of water (1000 kg/m³) and h is the height of water above the center of the orifice (8 ft + 1.2 m).
Similarly, the pressure at the downstream side can be calculated using the formula: P = ρgh.
Here, ρ is the density of oil (800 kg/m³) and h is the height of oil above the center of the orifice (5 ft).
Using the given coefficients of discharge (Cd), we can calculate the discharge through the orifice using the formula:
Q = Cd * A * √(2gΔh),
where A is the area of the orifice (πr², r is the radius of the orifice in meters), and Δh is the difference in pressure head (h2 - h1).
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