The Wind Pressure on Sails of a Sailboat

15 Sep 2022

Formula for Wind Pressure Calculation:

The wind pressure on the sails of a sailboat varies proportionally with the area of the sails and the square of the wind speed. The formula to calculate this is:

p = kA × v²

Where: - p is the wind pressure - k is the constant of proportionality - A is the area of the sails - v is the wind speed To determine the wind speed when the pressure on a square yard is 36 pounds, we can follow these steps:

Calculation:

Given: - Pressure on a square foot = 1 pound - Wind speed = 16 miles per hour Using the given information, we can establish the equation: 1 lb/ft² = k × 1 ft² × (16 mph)² Next, calculate the pressure when the area is converted to square yards: - Pressure on a square yard = 36 pounds - 1 yard = 3 feet Therefore, - Pressure on a square foot = 36 lb/yard² × (1 yard / 3 feet)² = 4 lb/ft² - Area of a square yard = 1 yard² × (3 feet / yard)² = 9 ft² Now, we have: 4 lb/ft² = k × 9 ft² × v² By dividing this equation with the previous equation, we can eliminate the constant, k, and solve for the wind speed: v² = 4 × (16 mph)² / 9 v = 2 × 16 mph / 3 v ≈ 10.7 mph ≈ 11 mph Therefore, the wind speed when the pressure on a square yard is 36 pounds is approximately 11 mph.

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