Natural flow phenomena can be modeled using elementary potential flows. Specifically, tornadoes and whirlpools in bathtub drains, sinks, etc. can be modeled quite realistically in 2D using the superposition of a vortex and a sink. (a) Write down the velocity potential of a tornado modeled as the superposition of a vortex and a sink, both centered at the origin. (b) What are the velocity components of this flow in polar coordinates? (c) Assuming inviscid flow of air at sea level, calculate the sink strength m for this flow if the vortex has strength =8000m/s2 and the pressure at a radius r=50m from the center is 98kPa