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A square tube 1.0 cm on a side gradually changes shape to become a circular tube 1.0 cm in diameter. Gasoline flows through the tube at 0.35 L/s.

Part A: What is the flow speed in the square tube? Express your answer with the appropriate units.
Part B: What is the flow speed in the circular tube? Express your answer with the appropriate units.
Part C: What is the pressure difference between the square tube and the circular tube? Express your answer with the appropriate units.

User Salyh
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Final answer:

To find the flow speed in the square tube, we can use the equation Flow rate = speed × cross-sectional area. The flow speed in the circular tube can be determined using the same equation but with the cross-sectional area calculated using the formula for a circle. The pressure difference between the square tube and the circular tube can be calculated using Bernoulli's equation.

Step-by-step explanation:

To determine the flow speed in the square tube, we can use the equation:

Flow rate = speed × cross-sectional area

The cross-sectional area of a square tube is equal to the side length squared. So for the square tube with a side length of 1.0 cm, the cross-sectional area is 1.0 cm².

Given a flow rate of 0.35 L/s, we can convert it to cm³/s by multiplying by 1000 (since 1 L = 1000 cm³).

Therefore, the flow speed in the square tube is:

Flow speed = Flow rate / Cross-sectional area = (0.35 cm³/s) / (1.0 cm²)

For the circular tube, the cross-sectional area is given by the formula:

Cross-sectional area = π × (diameter/2)²

Substituting the values, we get the cross-sectional area of the circular tube.

The flow speed in the circular tube is then:

Flow speed = Flow rate / Cross-sectional area = (0.35 cm³/s) / (formula for cross-sectional area of circular tube)

To find the pressure difference between the square tube and the circular tube, we can use Bernoulli's equation:

Pressure difference = (1/2) × (density of the fluid) × ((flow speed in circular tube)² - (flow speed in square tube)²)

User Dibyo Majumdar
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