Fluid Dynamics: Basic Concepts, Gate Discharge, and Flow Stability

Fluid Dynamics: Basic Concepts, Gate Discharge, and Flow Stability

DOI: 10.4018/978-1-5225-3079-4.ch003
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A review of basic fluid dynamics is presented in this chapter. Fluid static loading of hydraulic gates is examined. The focus in the present context will be on one-dimensional, incompressible flow of Newtonian fluids (air and water). Viscous effects will be included as loss coefficients in pressure drop calculations through ducts and channels. Discharge coefficients of hydraulics gates are presented to account for viscous effects in the flow past these gates. More advanced concepts related to the instabilities of boundary layers and free shear layers, and transition to turbulence will be introduced briefly and references provided for further investigation by the interested reader. Readers are encouraged to review additional fluid dynamic concepts using the text with which they are most comfortable.
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Fluid Properties

The properties of fluids that are relevant to gate vibrations include:

  • Fluid density, ρ (mass per unit volume)

  • Specific weight, 978-1-5225-3079-4.ch003.m01 (weight per unit volume)

  • Specific gravity, SG (ratio of the density of the given fluid to that of water under standard conditions)

  • Dynamic viscosity, μ (resistance to flow due to an imposed shear stress)

  • Kinematic viscosity, 978-1-5225-3079-4.ch003.m02 (a measure of the fluid’s ability to diffuse momentum)

Density, Specific Weight, and SG: For all liquids and for gases flowing at relatively low velocities, the density is assumed constant and the fluid is said to be incompressible. For gases, the ideal gas law, 978-1-5225-3079-4.ch003.m03 (with p = absolute pressure, R = the gas constant for each specific gas, and T = absolute temperature), is used to determine the gas density. For gases, the changes in pressure and temperature due to gas compressibility effects can usually be neglected for Mach numbers (see Table 1 for definition) less than about 0.3. Unless otherwise specifically noted, this book assumes fluids are incompressible. Once density is known, the specific weight and specific gravity can be found by multiplying by the acceleration or gravity, or by dividing by the standard density of water (1000 kg/m3 or 62.4 lbm/ft3), respectively.

Viscosity: For gases, the dynamic viscosity, μ, increases with increasing temperature; for liquids, dynamic viscosity decreases with increasing temperature. Dynamic viscosity does not vary significantly with pressure. Since the density of gases varies with pressure, however, kinematic viscosity (μ = μ/ρ) of gases depends on pressure as well as on temperature. The kinematic viscosity of liquids is predominantly a function of temperature alone for a wide range of moderate pressures, up to hundreds to thousands of atmospheres for most liquids (Avallone & Baumeister, 1987).

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