Tubes, bubbles and falling balls

You will write functions for the standard calculations of surface tension and viscosity. One finds the rise of a liquid in a tube. One finds the excess pressure in a bubble. One finds the steady speed of a falling ball. One finds the flow rate through a tube. Each function takes its numbers in the units that a lab would use, and changes them to SI units inside.

The idea. $h = \dfrac{2\gamma\cos\theta}{\rho g r}$. The excess pressure is $\dfrac{2s\gamma}{r}$, with $s$ surfaces. The steady speed is $v = \dfrac{2r^2(\rho_s - \rho)g}{9\eta}$. The flow rate is $Q = \dfrac{\pi\Delta Pr^4}{8\eta L}$. Use $g = 9.81\ \text{m/s}^2$.

Your tasks.

1. Complete capillary_rise(gamma, theta, rho, r), with $\gamma$ in mN/m, $\theta$ in degrees, $\rho$ in kg/m³ and $r$ in mm. It returns $h$ in mm.
2. Complete bubble_pressure(gamma, r, surfaces), with $\gamma$ in mN/m and $r$ in cm. It returns the excess pressure in Pa.
3. Complete terminal_speed(r, eta, rho_ball, rho_liquid), with $r$ in mm and $\eta$ in Pa s. It returns the speed in cm/s.
4. Complete flow_rate(dP, r, eta, L), with $\Delta P$ in kPa, $r$ in mm, $\eta$ in mPa s and $L$ in cm. It returns the flow in mL/s.