Differential Cartesian Coordinates Into Cylindrical Coordinates

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Has to convert B6-1 into B6-2 Source Transport Phenomenon 2nd ed -

sxgd39.jpg
 
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I can't even start solution
No idea how to convert subscipt from vx to vr and or to vtheta?
 
You are to find the radial component of the transport equation.

Set up the relevant quantities and relationships, then we'll help you.
 
In the first equation: substitute Vx = Vr * Cos (theta) Vy = Vr * Sin (theta) Vz = Vz

but how do I get V(theta)
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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