Question

The u velocity component of a steady, two-dimensional, incompressible flow field is u = 3 ax 2 - 2 bxy, where a and b are constants. Velocity component v is unknown. Generate an expression for u as a function of x and y.

Answer 1

Answer:

The velocity component v is $-6axy+2by^2+f(x)$

Explanation:

Given that,

The velocity component of a steady, two-dimensional

$u=3ax^2-2bxy$

We need to calculate the function of x

Using given equation

$u=3ax^2-2bxy$

Where, a and b is constant

On differential

$\dfrac{du}{dx}=6ax-2by$

We need to calculate the velocity component v

Using equation of velocity

$\dfrac{dv}{dy}=-\dfrac{du}{dx}-\dfrac{dw}{dz}$

Put the value into the formula

$\dfrac{dv}{dy}=-6ax+2by-0$

Now, on integration w.r.t y

$v=-6axy+2by^2+f(x)$

Hence, The velocity component v is $-6axy+2by^2+f(x)$