Hurricane Fluid flow, torque, cross product

1. The problem statement, all variables and given/known data
In 1993 the radius of Hurricane Emily was about 350 km. The wind speed near the center ("eye") of the hurricane, whose radius was about 30 km, reached about 200 km/h. As air swirled in from the rim of the hurricane toward the eye, its angular momentum remained roughly constant.

Estimate the wind speed at the rim of the hurricane.

r1 = 30km
v1 = 200 km/h
r2 = 350km

2. Relevant equations
I’m not entirely sure – it’s in a section where we are learning A1v1 = A2v2
Also – p1 + (rho)gy1 +1/2 rho v1^2 = p2 + rho(gy2) + 1/2(rho)v2^2

3. The attempt at a solution
I’m not entirely sure where to start – I actually have already completed this problem but am coming back to it a week later having forgotten what I learned. I just remember it was pretty simple if you took into account a relationship with the cross product.

I want to know how to understand the cross product to solving problems in general – I only kindof understand how to use the cross product, yet it is the basis of many things.

I know that it yields a perpendicular vector to two vectors – but for example in concepts like torque I have no freaking idea what it means to have the torque vector coming out of the page when in my mind a system will clearly be rotating clockwise or counter-clockwise on the page.

I’m stuck on the concepts of two other problems aswell – – I understand how the axis is being used but I don’t understand why it can be used that way.

A similar sort of concept is with a cow gate problem –

I can more or less follow what is being done but I want to be able to think through them without any guidance.

Essentially – Are there general strategies of thinking of torque and the cross product on 2d and 3d surfaces? Do you know of any equations or tools that will help make it more intuitive for me?

Leave a comment

Your email address will not be published.


Show Buttons
Hide Buttons