Using the figure as a guide, transform Cartesian velocity components (u,v,w)(u, v, w) into cylindrical velocity components (ur,uθ,uz)\left(u_r, u_\theta, u_z\right). (Hint: Since the zz-component of velocity remains the same in such a transformation, we need only to consider the xyx y-plane.)


Answered 2 years ago
Answered 2 years ago
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In given figure P9-10, when we apply trigonometry, it is clear that angle θ\theta is between uu and uru_r and also between vv and uθu_\theta.

Due to this, components of velocity in cylindrical coordination are:

ur=ucosθ+vsinθurcomponent of velocity\begin{align} \boxed{u_r = u \cdot \cos\theta + v \cdot \sin\theta \to u_{r} \text{component of velocity}} \end{align}

uθ=usinθ+vcosθuθcomponent of velocity\begin{align} \boxed{u_\theta = - u\cdot \sin\theta + v \cdot \cos\theta \to u_\theta\text{component of velocity}} \end{align}

uz=wz component of velocity\begin{align} \boxed{u_z = w \to \text{z component of velocity}} \end{align}

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