Fluid mechanics study guide (Cheat sheet)
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This document contains study guide information for a fluid mechanics course. It summarizes key concepts from the first two chapters, including definitions of density, specific weight, specific gravity, viscosity, shear stress, shear strain, and the ideal gas law. It also covers fluid pressure, Pascal's law, hydrostatic pressure equations, atmospheric pressure, gauge pressure, manometer equations, and calculations of hydrostatic forces on surfaces immersed in fluids.
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![Dennis Albert June 4, 2018
www.dennisusa.com
Chapter 2 Fluid Statics
Pressure: p =
𝒅𝑭
𝒅𝑨
Pressure can have units of Pa = N/m2, psf = lbf/ft2, psi = lbf/in2
P = F/A = ghA = hA
Pascal’s Law: Pressure at a point in a fluid at rest, or in motion, is independent of direction, as
long as there are no shearing stress present.
Pressure of fluid at rest: dP = - *dZ Z = elevation
𝑑𝑃
𝑑𝑍
= −
Incompressible fluid (constant fluid density):
𝑑𝑃
𝑑𝑍
= −
P1 – P2 = − (Z2 – Z1)
P1 – P2 = ∗ h, h=Z2-Z1
Compressible fluid (fluid density changes with temperature and pressure):
P2 = P1exp[- 𝑔(𝑍2−𝑍1)
𝑅𝑇0
]
Atmospheric pressure (measured by barometer): Patm = h + Pvapor
Gauge pressure (measured by manometer): p = h + p0
Manometer rule: p1 + *hdown - *hup = p2
Hydrostatic force on a plane surface: FR = p*A (FR: resultant force)
FR = hc *A (hc is the vertical distance from the fluid surface to the centroid of the area)
Location of the resultant force on x axis: yR = IXC/ycA + yc
Location of the resultant force on y axis: xR = IXC/xcA + xc](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
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The document discusses pressure and fluid statics. It defines pressure as a normal force exerted by a fluid per unit area. Atmospheric pressure is the pressure exerted by the atmosphere, while absolute and gauge pressures are defined in relation to a vacuum. Pressure at a point in a fluid is independent of direction and is a scalar quantity. The pressure in a stationary, incompressible fluid varies with depth due to gravity and can be calculated using equations that take into account fluid density and height. Pressure also varies with temperature for compressible fluids like gases based on the ideal gas law and assumptions about temperature changes over altitude. Standard atmospheric models and various pressure measurement techniques are also covered.
Chap 02
This document presents the basic flow equations, including the Navier-Stokes equation and Euler's equations for frictionless flow. It also introduces several dimensionless numbers that are used to characterize different types of fluid flow and heat and mass transfer, such as the Reynolds number, Prandtl number, Schmidt number, and more. These equations and numbers provide a theoretical framework for analyzing fluid flow, while practical applications require further assumptions and simplifications.
01 manometers
This document discusses fluid statics and manometers. It begins with reviewing key concepts such as pressure, density, states of matter, viscosity, and surface tension. It then covers the relationship between pressure, density, and depth in static fluids. Pressure is independent of direction and increases with depth due to the weight of the fluid above. Manometers use measured height differences of fluids in tubes to calculate pressure differences. The document provides examples of calculating pressures and pressure differences using various manometer setups and fluid properties.
Fluid (8 MAY 2020).pdf
This document discusses fluid mechanics concepts including fluid statics, fluid dynamics, and the equation of continuity. Key points covered include:
- Fluid statics concepts such as density, pressure, buoyancy force.
- Fluid dynamics concepts such as laminar vs turbulent flow and the equation of continuity.
- Ideal fluid flow assumptions including steady, nonviscous, incompressible, and irrotational flow.
- Examples calculating pressure, buoyancy force, fluid flow rates, and more.
fluid statics
This document discusses various topics related to fluid mechanics including:
1. Fluid statics, hydrostatic pressure variation, and Pascal's law.
2. Different types of pressures like atmospheric pressure, gauge pressure, vacuum pressure, and absolute pressure.
3. The hydrostatic paradox and how pressure intensity is independent of the weight of fluid.
4. Different types of manometers used to measure pressure like piezometers, U-tube manometers, single column manometers, differential manometers, and inverted U-tube differential manometers.
5. How bourdon tubes and diaphragm/bellows gauges can be used to measure pressure by converting pressure differences into mechanical displacements.
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- 1. Dennis Albert June 4, 2018 www.dennisusa.com Fluid Mechanics Study Guide Chapter 1. Fundamental concepts Density: = 𝑚 𝑉 Specific weight: = 𝑊 𝑉 = g Specific gravity: SG = (ref) = (ref) Ideal gas law: p = RT (R=286.9J/kg.K, J=N.m) Bulk modulus (a measure of the amount by which a fluid offers a resistance to compression): E = - 𝑑𝑃 𝑑𝑉/𝑉 Viscosity: mass/(time*length) Shear stress (the motion which is a consequence of the shearing effect within the fluid caused by the plate): = 𝑑𝐹 𝑑𝐴 = * 𝑑𝑢 𝑑𝑦 Shar strain (the shear stress causes each element to deform into shape of a parallelogram, the resulting deformation is defined by its shear strain, specified by the small angle ): = tan = x y Newton’s law of viscosity: = * 𝑑𝑢 𝑑𝑦
- 2. Dennis Albert June 4, 2018 www.dennisusa.com Chapter 2 Fluid Statics Pressure: p = 𝒅𝑭 𝒅𝑨 Pressure can have units of Pa = N/m2, psf = lbf/ft2, psi = lbf/in2 P = F/A = ghA = hA Pascal’s Law: Pressure at a point in a fluid at rest, or in motion, is independent of direction, as long as there are no shearing stress present. Pressure of fluid at rest: dP = - *dZ Z = elevation 𝑑𝑃 𝑑𝑍 = − Incompressible fluid (constant fluid density): 𝑑𝑃 𝑑𝑍 = − P1 – P2 = − (Z2 – Z1) P1 – P2 = ∗ h, h=Z2-Z1 Compressible fluid (fluid density changes with temperature and pressure): P2 = P1exp[- 𝑔(𝑍2−𝑍1) 𝑅𝑇0 ] Atmospheric pressure (measured by barometer): Patm = h + Pvapor Gauge pressure (measured by manometer): p = h + p0 Manometer rule: p1 + *hdown - *hup = p2 Hydrostatic force on a plane surface: FR = p*A (FR: resultant force) FR = hc *A (hc is the vertical distance from the fluid surface to the centroid of the area) Location of the resultant force on x axis: yR = IXC/ycA + yc Location of the resultant force on y axis: xR = IXC/xcA + xc