From wikipedia on the Venturi effect:
Relationship between pressure and flow speed
An equation for the drop in pressure due to the Venturi effect may be derived from a combination of Bernoulli's principle and the continuity equation.
Referring to the diagram to the right, using Bernoulli's equation in the special case of incompressible flows (such as the flow of water or other liquid, or low speed flow of gas), the theoretical pressure drop at the constriction is given by:
p_1  p_2 = \frac{\rho}{2}\left(v_2^2  v_1^2\right)
where \scriptstyle \rho\, is the density of the fluid, \scriptstyle v_1 is the (slower) fluid velocity where the pipe is wider, \scriptstyle v_2 is the (faster) fluid velocity where the pipe is narrower (as seen in the figure). This assumes the flowing fluid (or other substance) is not significantly compressible  even though pressure varies, the density is assumed to remain approximately constant.
