A fluid passing through smoothly varying constrictions is subject to changes in velocity and pressure, as described by Bernoulli's principle. In case of fluid or airflow through a tube or pipe with a constriction in it, the fluid must speed up in the restriction, reducing its pressure, and producing a partial vacuum.
As shown in the Fig.1 fluid density = (ρ), area = (A), and velocity = (V). Let the properties of fluid at entrance and exit be ( ρ1, A1, V1) and at constriction be (ρ2, A2, V2). There is a drop in pressure at the constriction as shown by the height of the column and it is due to conservation of energy. The fluid experiences a gain in kinetic energy and a drop in pressure as it enters the constriction; this effect is called Venturi effect, it is named after the Italian physicist Giovanni Battista Venturi.
Continuity Equation
It is simply a mathematical expression of the principle of conservation of mass. Mass is neither created nor destroyed. For a steady flow, it states that:
The "continuity equation” is a direct consequence of the rather trivial fact that what goes into the pipe must come out. This has the important consequence that as the area of the hole decreases, the velocity of the fluid must increase, in order to keep the flow rate constant.
Specific Weight, Density, and Specific Gravity
(a) Specific Weight or Weight Density
The weight per unit volume of a substance. Usually it is expressed in N/m3 or lbs/ft3. Mathematically,
(b) Density
Density is defined as the ratio of the mass of an object to its volume; usually it is expressed in kg/m3 or g/cm3. Mathematically,
(c) Specific Gravity
The ratio of the density (or specific weight) of a substance to the density (or specific weight) of a standard fluid is called Specific gravity or Relative density. The usual standard of comparison for solids and liquids is water at 4°C at atmospheric pressure. Gases are commonly compared to dry air, under standard conditions (0°C and atmospheric pressure).
Specific gravity is not expressed in units, as it is purely a ratio. Mathematically,
Compressibility and Bulk Modulus
Compressibility is the measure of change in volume of substance when pressure is exerted on it. Liquids are incompressible fluids. For each atmosphere increase in pressure, the volume of water would decrease 46.4 parts per million. The hydraulic brake systems used in most cars operate on the principle that there is essentially no change in the volume of the brake fluid when pressure is applied to this liquid.
On the other hand, the volume of the gases can be readily changed by exerting an external pressure on the gas. An internal combustion engine provides a good example of the ease with which gases can be compressed.
The compressibility is the reciprocal of the bulk modulus. Compressibility is denoted by "k" and is expressed mathematically as:
Where B is called the bulks modulus of elasticity and is defined as the ratio of change in pressure to volumetric strain (change in volume/original volume) over a fluid element. It is expressed as follows:
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Viscosity and Viscosity Index
Viscosity is the measure of the internal friction of a fluid or its resistance to flow. A hydraulic fluid that is too viscous usually causes high-pressure drop, sluggish operation, low-mechanical efficiency, and high-power consumption. Low-viscosity fluids permit efficient low-drag operation, but tend to increase wear, reduce volumetric efficiency, and promote leakage.
Viscosity index is an arbitrary scale, which indicates how the viscosity of a fluid varies with changes in temperature. The higher the viscosity index, the lower the viscosity changes with respect to temperature and vice versa. Ideally, the fluid should have the same viscosity at very low temperatures as well as at high temperatures. In reality, this cannot be achieved. This change is common to all fluids. Heating tend to make fluids thinner and cooling makes them thicker.