Laser Doppler Velocimetry $($LDV$)$ is a powerful tool in measuring instantaneous velocities in transparent media. Suppose an LDV system is employed to measure z$-$component of velocity $(u_z)$ at a certain point in a tubular flow of water at $20C.$ Time versus velocity readings are listed below. Inside tube diameter is $5cm$ and volumetric flow rate is measured as $15\frac{m^3}{h}.$

$\backslash$table$[[$time $(s),0\mathrm{.}5,1\mathrm{.}0,1\mathrm{.}5,2\mathrm{.}0,2\mathrm{.}5,3\mathrm{.}0,3\mathrm{.}5,4\mathrm{.}0,4\mathrm{.}5,5\mathrm{.}0],[u_z(\frac{m}{s}),1\mathrm{.}84,1\mathrm{.}77,1\mathrm{.}82,1\mathrm{.}86,1\mathrm{.}88,1\mathrm{.}84,1\mathrm{.}90,1\mathrm{.}80,1\mathrm{.}82,1\mathrm{.}87]]$

a$)$ Calculate the intensity of turbulence.

b$)$ What is the distance between the measurement point and the center of the tube?