Find the radial component and tangential component of the fluid’s velocity.
A thin long circular pipe of 10 mm diameter has porous walls and spins at 60 rpm about its own axis. Fluid is pumped out of the pipe such that it emerges radially relative to the pipe surface at a velocity of 1 m/s.
What is the radial component of the fluid’s velocity at a radial location 0.5 m from the pipe axis?
What is the tangential component of the fluid’s velocity at the same radial location as above?
a) Here we can consider flow as a 2D flow .Using the continuity equation we get
\(A_{1}V_{r1}=A_{2}V_{r2}
\\\Rightarrow \pi d_{1}v_{r1}=\pi d_{2}v_{r2}
\\\Rightarrow v_{r2}=\frac{1\times 0.01}{0.05\times 2}
\\=0.01\;m/s\)
Therefore radial component of fluid velocity is \(0.01 \;m/s\)
b) The tangential velocity of the fluid is constant.
\(\Rightarrow v_{\theta }=60\times \frac{2\pi}{60}\times 0.005
\\=0.0314\;m/s\)
Tangential component of fluid velocity is \(0.0314 \;m/s\)
