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A U-tube contains water and oil. The oil of density 800kg / (m ^ 3) rest on the surface of the water in the right-hand leg to a depth of 5cm. if the level of water in the left hand leg is 10cm above the level of water in the right hand leg, determine the pressure difference between the two legs. The density of water is 1000kg / (m ^ 3)

Question

A U-tube contains water and oil. The oil of density 800kg / (m ^ 3) rest on the surface of the water in the right-hand leg to a depth of 5cm. if the level of water in the left hand leg is 10cm above the level of water in the right hand leg, determine the pressure difference between the two legs. The density of water is 1000kg / (m ^ 3)

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Solution

To solve this problem, we need to calculate the pressure at the bottom of each leg of the U-tube and then find the difference.

Step 1: Calculate the pressure at the bottom of the right-hand leg.

The pressure at the bottom of the right-hand leg is due to the weight of the oil and the water above it. The pressure due to a fluid column is given by the equation P = ρgh, where ρ is the density of the fluid, g is the acceleration due to gravity, and h is the height of the fluid column.

For the oil, ρ = 800 kg/m^3, g = 9.81 m/s^2, and h = 0.05 m (since 5 cm = 0.05 m). So, the pressure due to the oil is P_oil = 800 kg/m^3 * 9.81 m/s^2 * 0.05 m = 392.4 Pa.

For the water in the right-hand leg, ρ = 1000 kg/m^3, g = 9.81 m/s^2, and h = 0.10 m (since 10 cm = 0.10 m). So, the pressure due to the water is P_water_right = 1000 kg/m^3 * 9.81 m/s^2 * 0.10 m = 981 Pa.

So, the total pressure at the bottom of the right-hand leg is P_right = P_oil + P_water_right = 392.4 Pa + 981 Pa = 1373.4 Pa.

Step 2: Calculate the pressure at the bottom of the left-hand leg.

The pressure at the bottom of the left-hand leg is due to the weight of the water above it. For the water in the left-hand leg, ρ = 1000 kg/m^3, g = 9.81 m/s^2, and h = 0.20 m (since 20 cm = 0.20 m). So, the pressure due to the water is P_water_left = 1000 kg/m^3 * 9.81 m/s^2 * 0.20 m = 1962 Pa.

Step 3: Find the pressure difference.

The pressure difference between the two legs is ΔP = P_left - P_right = 1962 Pa - 1373.4 Pa = 588.6 Pa.

This problem has been solved

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