A Venturi Meter is a device used to measure the flow speed of a fluid in a pipe. At the throat, the are is reduce from (A) to (a) and the velocity is increased from (v) to (V). Note that at the throat where the velocity is the greatest, the pressure is least. This is we know is true from Bernoulli's equation which is:
p(1) +1/2pv*v + pgy(1) = p(2) +1/2pv*v + pgy(2)
This equation addresses the conservation of energy involving a fluid.
We can use a form of this equation and the equation of contuinuity, A*v = const, to say that
v = A*sqrt[(2*a*a*dp)/(density*(A*A - a*a))]