Approximating Windshield Shape of a Car: Velocity at Points A & B

[kela582]

Homework Statement

[/B]
The shape of a car windshield is approximated in the figure below; its length is 2.0 ft and height is 1.5 ft. Obtain an equation of the windshield shape r as a function of
θ,
r(θ), in the polar coordinate system shown in the picture.

When the car moves at 55 mph, determine the velocity of the air at points A and B.

Homework Equations

Not really sure how to approach this...maybe Bernoulli's Equation? We've been studying the method of repeating variables, but I'm unsure how I would apply that. I really don't know where to begin with this one!

The Attempt at a Solution

(P/rho + v^2/2 + gz = constant)
But I don't know the pressure difference...I'm hopelessly stuck :( If anyone could help shed some light on this, and just give me an idea where to even begin, that would be very appreciated!

 

[Chestermiller]

This seems to be a trick question. Have you heard of the "no slip" boundary condition?

Chet

 

[kela582]

This seems to be a trick question. Have you heard of the "no slip" boundary condition?

Chet

Ah, so v_A = 0.

 

[Chestermiller]

Ah, so v_A = 0.

Relative to the car. Relative to the ground, it's U = 55 mph.

Chet

 

[rezeew]

I would approach this problem by first understanding the physical principles involved. The shape of the windshield is important because it affects the flow of air around the car, which can impact the car's aerodynamics and fuel efficiency.

To obtain an equation for the windshield shape, I would start by breaking it down into simpler geometric shapes, such as circles, lines, and curves. Using these shapes, I would create a mathematical model that describes the windshield's shape in terms of its length, height, and angle θ.

Next, I would use Bernoulli's equation to analyze the air flow at points A and B. This equation relates the pressure, velocity, and height of a fluid and can be used to calculate the velocity of the air at these points. I would also take into account the speed of the car, as it will affect the overall air flow around the car.

To solve for the velocity at points A and B, I would use the equation for the windshield shape and the values for the car's speed and angle θ. I would also consider any other factors that may affect the air flow, such as the shape and size of the car's body.

Overall, this problem requires a combination of mathematical modeling and understanding of fluid dynamics principles. As a scientist, it is important to approach problems like this with a systematic and analytical mindset, using both theoretical knowledge and practical considerations to find a solution.