Ch 14: Fluids and Elasticity

Knight Calc - Physics for Scientists and Engineers 5th Edition

Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Not the one you use?Change textbook

Knight Calc 5th Edition

Ch 14: Fluids and Elasticity

Problem 61b

Chapter 14, Problem 61b

A hurricane wind blows across a 6.0 m x 15.0 m flat roof at a speed of 130 km/h. What is the pressure difference?

Verified step by step guidance

Step 1: Convert the wind speed from km/h to m/s for consistency in SI units. Use the conversion factor: 1 km/h = 0.27778 m/s. Multiply 130 km/h by 0.27778 to get the wind speed in m/s.

Step 2: Apply Bernoulli's principle to determine the pressure difference. Bernoulli's equation states that the pressure difference is related to the change in velocity: ΔP = (1/2)ρv², where ρ is the density of air (approximately 1.225 kg/m³ at sea level) and v is the wind speed in m/s.

Step 3: Substitute the values into the formula ΔP = (1/2)ρv². Use ρ = 1.225 kg/m³ and the wind speed converted in Step 1.

Step 4: Calculate the pressure difference ΔP using the formula derived in Step 3. Ensure all units are consistent (kg, m, s).

Step 5: Interpret the result. The pressure difference calculated represents the force per unit area exerted by the wind on the roof due to the change in velocity.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Bernoulli's Principle

Bernoulli's Principle states that an increase in the speed of a fluid occurs simultaneously with a decrease in pressure. In the context of a hurricane, as the wind speed increases over the roof, the pressure above the roof decreases compared to the pressure inside the building, leading to a pressure difference that can cause structural damage.

Pressure Difference

Pressure difference refers to the variation in pressure between two points in a fluid. In this scenario, the pressure difference between the inside of the building and the wind-exposed roof can be calculated using Bernoulli's equation, which relates the speed of the wind to the resulting pressure exerted on the roof.

Conversion of Units

In physics problems, it is often necessary to convert units to maintain consistency. Here, the wind speed is given in kilometers per hour, which should be converted to meters per second for calculations involving pressure, as the standard unit of pressure (Pascals) is derived from SI units. This conversion is crucial for accurate results.

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Related Practice

Textbook Question

Water from a vertical pipe emerges as a 10-cm-diameter cylinder and falls straight down 7.5 m into a bucket. The water exits the pipe with a speed of 2.0 m/s. What is the diameter of the column of water as it hits the bucket?

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Textbook Question

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Textbook Question

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