A venturi meter with a 3 -in. -diameter throat is placed in...

A venturi meter with a 3 -in. -diameter throat is placed in a 6 -in.-diameter line carrying water at $75^{\circ} \mathrm{F}$, The pressure drop between the upstream tap and the venturi throat is 12 in. of mercury. Compute the rate of flow.

Key Concepts

Venturi Meter

A Venturi meter is a flow measurement device that utilizes a converging section, a throat, and a diverging section to create a pressure difference that can be measured. The design causes an increase in velocity and corresponding decrease in pressure in the throat, which can then be related to the flow rate using fluid dynamics principles.

Bernoulli’s Principle

Bernoulli’s principle states that within a streamline flow of an incompressible fluid the sum of the pressure energy, kinetic energy, and potential energy remains constant. This principle is applied in the venturi meter to relate the drop in pressure to an increase in velocity, which is crucial for determining the flow rate.

Continuity Equation

The continuity equation is based on the conservation of mass, stating that the mass flow rate must remain constant in a steady, incompressible flow. This relation between different cross-sectional areas of the pipe allows us to connect the velocity of the fluid in the larger section to that in the throat, thus enabling accurate flow rate calculation.

Differential Pressure Measurement

Differential pressure measurement involves gauging the pressure difference between two points in a flow system. In the context of a Venturi meter, this measured pressure drop is a key parameter used to infer the fluid’s velocity and, subsequently, the volumetric flow rate through the device.

Unit Conversion

Unit conversion is an essential process in fluid mechanics problems to ensure that all physical quantities are expressed in consistent units. This is particularly important when the measured pressure drop or other quantities are given in non-standard units, such as inches of mercury, which must be converted to compatible units like Pascals or psi for calculations.

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