What is a venturi-meter? Explain its construction and working.

(N/A) venturi-meter is a device used to measure the flow speed of an incompressible fluid.
Construction:
It consists of a tube with a broad diameter and a small contraction at the middle,known as the throat,as shown in the figure. $A$ manometer in the form of a $U$-tube is attached to it,with one arm at the broad section of the tube and the other at the throat.
Working:
The manometer contains a liquid of density $\rho_{m}$. Let the density of the flowing fluid be $\rho$.
At point $1$,the cross-sectional area is $A$ and the velocity of the liquid is $v_{1}$. At point $2$ (the throat),the cross-sectional area is $a$ and the velocity of the liquid is $v_{2}$.
According to the equation of continuity:
$A v_{1} = a v_{2}$
$\therefore v_{2} = \frac{A v_{1}}{a}$
Applying Bernoulli's equation at points $1$ and $2$ (assuming horizontal flow,$h_{1} = h_{2}$):
$P_{1} + \frac{1}{2} \rho v_{1}^{2} = P_{2} + \frac{1}{2} \rho v_{2}^{2}$
$\therefore P_{1} - P_{2} = \frac{1}{2} \rho (v_{2}^{2} - v_{1}^{2})$
From the manometer reading,the pressure difference is given by:
$P_{1} - P_{2} = \rho_{m} g h$
Equating the two expressions for pressure difference:
$\rho_{m} g h = \frac{1}{2} \rho (v_{2}^{2} - v_{1}^{2})$
Substituting $v_{2} = \frac{A v_{1}}{a}$ allows for the calculation of the flow velocity $v_{1}$.