CIVL $3510$: Fluid Mechanics

Fall$-2024$

Instructor: Dr$.$ Ram Balachandar

Assignment $-2$

Consider the following steady, two$-$dimensional velocity field:

Is there a stagnation point in this flow field? If so$,$ where is it$?$

Consider the flow field given below:

vec$(V)=(u,v)=(U_0+bx)vec(i)-$byvec$(j)$

Calculate the material acceleration for the given flow field?

Consider the steady flow of water through an axisymmetric garden hose nozzle $($Fig$.1).$

Along the centerline of the nozzle, the water speed increases from $U_{\text{e}\text{n}\text{t}\text{r}\text{a}\text{n}\text{c}\text{e}}$ to $U_{\text{e}\text{x}\text{i}\text{t}}$ as

sketched. Measurements reveal that the centerline water speed increases parabolically

through the noczle. Write an equation for centerline speed $u(x),$ based on the parameters

given here, from $x=0$ to $x=L.$

$($Hint : A general equation for parabola in x is : $u=a+b(x-c{)}^2)$

Fig. $1$ Flow through nozzle