# Aerodynamics: Find Expressions for u and v

• shreddinglicks
In summary, the conversation discusses finding expressions for u and v using the given equations for the absolute value of velocity and the equation of streamlines in a velocity field. The solution involves taking the partial derivative and making assumptions to keep the ratio of u to v consistent.
shreddinglicks

## Homework Statement

The absolute value of the velocity and the equation of the streamlines in a velocity field are given, respectively,

|V|=sqrt(x^2+2xy+2y^2) and y^2+2xy = C

Find expressions for u and v.

## Homework Equations

dy/dx = v/u
|v| = sqrt(u^2+v^2)

## The Attempt at a Solution

included in attachment

#### Attachments

• CCI01212017.jpg
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Most of your steps look good. Remember that
##u^2 = f(x,y) ##
implies
##u = \pm \sqrt{f(x,y)}.##
This is important because you need to be consistent and keep ##\frac vu = -1##.

Thanks, my only major concern is that when I take the partial derivative, how do I know which term to take derivatives in respect to y or x. Do I have to make assumptions?

## 1. What is aerodynamics?

Aerodynamics is the study of how objects move through air. It involves the analysis of forces and motion in relation to the flow of air over an object.

## 2. Why is understanding aerodynamics important?

Understanding aerodynamics is important in many fields, including aviation, automotive design, and sports. It allows for the optimization of design and performance in these areas.

## 3. What is the significance of finding expressions for u and v in aerodynamics?

Finding expressions for u and v, which represent the velocity components in the x and y directions, respectively, allows for the calculation of aerodynamic forces and the prediction of an object's motion through air.

## 4. How are u and v related to lift and drag?

Lift is directly related to the vertical component of velocity, v, while drag is directly related to the horizontal component of velocity, u. This means that changes in u and v can affect the lift and drag forces acting on an object.

## 5. What factors affect u and v in aerodynamics?

U and v can be affected by several factors, such as the shape and size of an object, the speed and direction of the air flow, and the properties of the air itself, such as density and viscosity.

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