# Consider an incompressible flow over a flat plate with the following approximation to the velocity profile: $\frac{u(y)}{U}=\left\{\begin{array}{l}\frac{y}{\delta} \text { for } y \leq \delta \\ 1 \text { for } y>\delta\end{array}\right.$ where $\delta$ is the boundary layer thickness and $U$ the free-stream speed. The normalized momentum thickness $(\theta / \delta)$ for this profile is________________(in three decimal places)

## Question ID - 155581 :- Consider an incompressible flow over a flat plate with the following approximation to the velocity profile: $\frac{u(y)}{U}=\left\{\begin{array}{l}\frac{y}{\delta} \text { for } y \leq \delta \\ 1 \text { for } y>\delta\end{array}\right.$ where $\delta$ is the boundary layer thickness and $U$ the free-stream speed. The normalized momentum thickness $(\theta / \delta)$ for this profile is________________(in three decimal places)

3537

Answer Key : (0.165 to 0.168) -

0.165 to 0.168

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An idealized velocity field is given by $\vec{V}=4 t x \hat{\imath}-2 t^{2} y \hat{\jmath}+4 x z \hat{k}$. At point (-1,1,0) and at $t=1,$ the magnitude of the material acceleration vector of the fluid element is______________