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Fluid Measurements

Viscometer

According to the definition of viscosity or Dynamic Viscosity, it can be determined by the shear stress and the rate of shear strain. By using a rotating motion instead of linear motion to the fluid viscosity testing experiment, a continuous motion can be applied.

Consider two concentric cylinders with a small gap in between and the velocity distribution of the fluid is linear.

Therefore, the viscosity can be determined by measuring the torque at a specified angular velocity.

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Fluid Properties

Compressibility

Compressibility is used to described the easy of volume change for a fixed massed of fluid due to a pressure change. Bulk modulus is usually used to characterize the compressibility in an analogous manner to Young's modulus of elasticity for solids. For a given mass, the volume change of a fluid is inversely proportional to its density. And the bulk modulus is expressed as

and can be approximated by a differential change as

or

For ideal gas compression or expansion under constant temperature,i.e. isothermal process,

imply

And for the compression or expansion is reversible and adiabatic, i.e. frictionless and no heat exchange with surroundings under isentropic process,

where ;

imply

If the pressure changes are small, gases can be treated as incompressible fluid.

Speed of Sound

Speed of sound which describe the speed of pressure wave propagation in the fluid, is an important parameter in compressible flow. When a piston moves forward, the generated pressure wave will travel through the fluid at the speed of sound . When the piston moves a constant incremental velocity , there will have a small increase in local pressure at the wave front and a small difference in the fluid states across the wave front. Considering a moving control volume that encloses the wave front,  fluid will move toward the wave front into the control volume at a relative speed of and fluid will also move away from the wave front and leave the control volume at a relative speed of

From the conservation of mass,

From the steady flow energy balance equation, by neglecting potential energy change and there is no heat or work crosses the boundaries,

Imply

The small disturbance can also be assumed as an isentropic process, imply

Therefore or

and it can be expressed as
or

and the seed of sound is a function of temperature only.

Mach Number

Mach number, Ma, is defined as the ratio of the fluid flow speed to the speed of sound in the same fluid at the same state, i.e. and is another important parameter in compressible flow.

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Fluid Properties

Vapor Pressure (P_v)

At a given pressure, a pure substance changes its phase at the saturation temperature, T_sat.

At a given temperature, a pure substance change its phase at the saturation pressure, P_sat.

At a given temperature, the enclosed liquid in a container will evaporate. In phase equilibrium, the pressure exerted by its vapor is named vapor pressure, P_v. For a pure vapor, it is identical to the saturation pressure of the liquid at the given temperature.

But when the vapor of the liquid is mixed with other gases, for example water vapor and dry air, the pressure caused by the water vaor is a partial pressure only. The atmospheric pressure will be the sum of the partial pressure of dry air and the partial pressure of water vapor.

In liquid flow system, the absolute liquid pressure may drop below the vapor pressure at some locations along the flow and cause unplanned locate vaporization, boiling and forms cavities in the liquid as vapor bubbles, named cavitation bubbles. As bubbles move away from the low-pressure regions, they will collapse and generate extremely high-pressure destructive waves. The formation and collapse of cavitation bubbles will cause the drop in performance and the erosion of component parts, for example irregular, narrowed flow passages of valve or pump, impeller blades of hydraulic turbine. And the formation and subsequent collapse of vapor bubbles in a flowing liquid is called cavitation.