Mechanical Engineering - Hydraulics and Fluid Mechanics - Discussion

Venturimeter is an instrument used to measure the discharge of liquid flowing in a pipe. It consists of three parts, i.e the converging cone, the throat and the diverging cone. The length of the divergent cone is made about three to four times convergent cone in order to avoid the tendency of breaking away the stream of liquid and to minimise frictional losses. It may be noted that

(a) The velocity of liquid at the throat is higher than that of the inlet.
(b) The pressure of the liquid at the throat is lower than that of the inlet.
(c) The velocity and pressure of the liquid flowing through the divergent portion decrease.

The discharge through a Venturimeter is given by;

Q = Cda1a2 √2gh/(a1^2 - a2^2).
where
Cd = Coefficient of discharge,
a1 = Area at inlet,
a2 = Area at the throat, and
h = Venturi-head.

Actually, in case of compressible fluid combining the BERNOULLI equation and CONTINUITY equation we get the resulting equation dA/A=-dV/V (1-Ma*2). In the divergent section of the venturi meter, the fluid velocity reaches beyond sonic velocity and attains a supersonic velocity and in such case with the increase in area pressure decreases and velocity increases. Since we generally consider liquid to be incompressible so we do not take into account this Ma factor in liquid flow but in case we consider liquid to be compressible we had to understand this peculiar behavior. SO THE GIVEN ANSWER C IS CORRECT.

Option B is CORRECT.

The velocity reaches its maximum value and pressure reaches its minimum value at the throat. Subsequently, a decrease in the velocity and an increase in the pressure takes place in course of flow through the divergent part. This typical variation of fluid velocity and pressure by allowing it to flow through such a constricted convergent-divergent passage was first demonstrated by an Italian scientist Giovanni Battista Venturi in 1797.

According to the continuity equation A1V1=A2V2, the velocity is inversely proportional to the cross-section, so the velocity decreases with the increase in the area.

-> Similarly, according to the Bernoulli theorem, the pressure is inversely proportional to the velocity of the moving particles.

Thus, this implies the divergent section of the venturi meter has less velocity with maximum pressure.

Yes @Prasad according to Bernoulli equation.

Summation of total energy of fluid at a point remains same.

So potential energy terms cancel out.

And according to continuity equation we know velocity will decrease with increase in area in diverging portion so as the kinetic energy increase and according to bernoulli eq pressure must decrease otherwise law of conservation of energy will be violent.

Option B is absolutely correct.

Av = constant implies as area increases velocity decreases.

From applications of Bernoulli equation we know, pressure α 1/velocity (pressure is inversely proportional to velocity, as velocity decreases pressure increases. As simple as that don't complicate it guys.

By continuity equation, the area is inversely proportional to velocity so with the increase in area in the diverging section velocity decreases and therefore by Bernoulli's equation we can conclude that the pressure must increase in this region.

The velocity reaches its maximum value and pressure reaches its minimum value at the throat. Subsequently, a decrease in the velocity and an increase in the pressure takes place in course of flow through the divergent part.

Pressure increases in divergent section that's why length of divergent section is increased so that pressure increases gradually else flow would not happen from low pressure region in throat to high pressure region.

From continuity equation: Area in divergent section increases correspond to the decrease in velocity.

And by Bernoulli's theorem, if kinematic head decreases correspond to the increase in pressure head.