Summary

Pressure difference between fluids causes flow.
A_1v_1=A_2v_2 expresses conservation of mass. Narrow area force faster speeds to incompressible fluids.
Bernoulli's equation: P_1+pgy_1+\frac{1}{2}pv_1^2=P_1+pgy_2+\frac{1}{2}pv_2^2 expresses conservation of energy along a streamline.
Faster fluid has lower pressure and vice versa
Torricelli's theorem: v=\sqrt{2g\Delta y} is derived from energy conservation and gives exit speed of draining fluid.
Assume fluids are ideal unless stated otherwise.