Fluid Mechanics Flashcards
[Formula] Specific Weight (γ)
γ = pg –> (density)(gravity)
[Formula] Force needed to move single-plate viscometer (F)
F = μvA/δ –> [(viscosity)(velocity)(area)] / thickness
[Formula] Force (F)
F = ma –> (mass)(acceleration)
[Formula] Mass (m)
m = pV –> (density)(volume)
[Formula] Height change due to capillary action (h)
h = (4σcosβ) /γd = (4σcosβ) /pgd
[Formula] Specific volume (υ)
υ = V/m –> volume/mass
υ = 1/p –> 1/density
Fluid Statics - Hydrostatic Pressure
[Formula] Pressure (P) for a stationary, incompressible fluid
P = pgh –> (density)(gravity)(height)
or
P = γh –> (specific weight)(height)
Archimedes Principle (Part 1)
- The buoyant force exerted on a submerged or floating body is equal to the weight of the fluid displaced by the body.
Archimedes Principle (Part 2)
- A floating body displaces a weight of fluid equal to its own weight; i.e., a floating body is in equilibrium.
[Formula] Bernoulli Equation
P2/γ + v2^2/2g + z2 = P1/γ + v1^2/2g + z1
Specific Gravtiy
What is specific gravity? (definition AND formula)
A dimensionless ratio of a fluid’s density to a standard reference density.
SG = p / p_Water (density/density of water) Also can use specific weight.
Pressure
What are “absolute pressures?”
Pressures measured with respect to a ‘true zero pressure.’
Pressure
What are “gage pressures?”
Pressure measured with respect to ‘atmospheric pressure.’
Pressure
How are absolute and gage pressures related? (Formula)
P_absolute = P_atmospheric + P_gage
Pressure
What is a ‘vacuum’ pressure measurement?
A pressure below atmospheric pressure (i.e., a negative gage pressure).
Stress
Stress has a different symbol in “Materials” than in “Fluids.” What are those symbols?
τ for fluids
σ for materials
Stress
How many primary types of stress are there?
What are they?
2 types:
normal stress – area is normal to the force
tangential (or shear) stress – area is parallel to the force
Stress
Ideal fluids that are inviscid and incompressible respond to what type of stress? What other type of stress can they not support?
Respond to normal stresses
Cannot support shear stresses
Viscosity
What is “viscosity?”
The measure of a fuild’s resistance to flow when acted upon by an external force, such as a pressure gradient or gravity.
Viscosity
What is the formula for viscosity of a Newtonian fluid?
τ = µ(dv/dy)
Viscosity
What is the formula for viscosity of a non-Newtonian fluid?
τ = K(dv/dy)^n
Viscosity
What is “kinematic viscosity?” (definition and formula)
Ratio of absolute viscosity to mass density.
v = µ/p = µg_c / p
(primary units: L^2 / θ)
Surface Tension
What is surface tension? (definition and formula)
Intermoluecular cohesive forces causing what seams to be a membrane.
σ = F/L
Capillarity
What is capillary action?
Behavior of a liquid in a thin-bore tube.
Specifically, it is caused by surgace tension between the liquid and a vertical solid surface.
Capillarity
What is the “angle of contact,” β?
An indication of whether adhesive or cohesive forces dominate.
β < 90 degrees, adhesive forces are dominant
β > 90 degrees, cohesive forces are dominant
Capillarity
What is the formula for capillary rise in a small-bore tube?
h = (4σcosβ/pgd_tube)
Fluid statics - Hydrostatic Pressure
What is hydrostatic pressure? (definition and formula)
The pressure a fluid exerts on an immersed object or on container walls.
p = F/A
Fluid statics - Hydrostatic Pressure
What is the Hydrostatic Paradox?
The pressure at depth h is independent of volume.
Fluid statics - P for a stationary, incompressible fluid
Pressure at a point as the same magnitude in all directions. What is this called?
Pascal’s law
Fluid statics- P for a stationary, incompressible fluid
Pressure is always what to a surface, regardless of shape or orientation?
Normal.
(This is a result of the fluid’s inability to support shear stress.)
Fluid Statics - Manometry
What is a manometer used for?
Indicating small pressure differences.
Fluid Statics - Manometry
What is a differential manometer?
What is an open manometer?
differential manometer - When both ends are connected to pressure sources.
open manometer - When one end is open tot he atmosphere.
Fluid Statics - Manometry
What is the formula for pressure difference in an open manometer?
P0 = P2 + p2gh2 - p1gh1
or
= P2 + γ2h2 - γ1h1
Fluid Statics - Manometry
What is the formula for pressure difference in an open manometer, where fluid 1 is absent or has a low density, or if distance h1 is so small as to be insignificant?
P2 - P0 = -p2gh2
or
= -γ2h2
Fluid Statics - Barometers
What is a barometer?
Device for measuring the absolute pressure of the atmosphere. Tube fluid is mercury.
Fluid Statics - Barometers
What is the atmospheric pressure equation when the fluid is mercury? (i.e., when the vapor pressure in the tube is neglected?)
Pa = pgh
or
= γh
Fluid Statics - Barometers
What is the atmospheric pressure equation when the fluid is NOT mercury? (i.e., when the vapor pressure in the tube is significant, such as with water or alcohol?)
Pa = Pv + pgh
or
= Pv + γh
Fluid Statics - Forces on Submerged Plane Surfaces
Total vertical force on a horizontal plane of area A (formula)
R = PA (resultant = pressure x area)
Fluid Statics - Forces on Submerged Plane Surfaces
Vertical rectangular plane surface:
Pressure increases linearly with depth.
* If the plane surface extends to the surface, what shape will the pressure distribution be?
* If it does not, what shape will it be?
- Triangular
- Trapezoidal
Fluid Statics - Forces on Submerged Plane Surfaces: Vertical Rectangular
What is the resultant force calculated from?
Average pressure. (located at the centroid)
Fluid Statics - Forces on Submerged Plane Surfaces
What is the average pressure formula for:
* vertical plane
* inclined plane
P = 1/2 γ(h1 + h2)
P = 1/2 γ(z3 + z4)sinα
(symbol for p should have horizontal line on top.)
Fluid Statics - Center of Pressure
Nonrectangular plane surface that* may or may not* extend to the liquid surface and that* may or may not* be inclined:
At P0 = 0, what is the formual for:
* average pressure
* Ycp (center of pressure on y axis)
* Zcp (center of pressure on z axis)
- P = pgZc(sinα) or γZcsinα
- Ycp - Yc = y* = (Iyz)/(A)(Zc)
- Zcp - Zc = z* = (Iy)/(A)(Zc)
Fluid Statics - Buoyancy
What is buoyancy?
An upward force that acts on all objects that are partially or completly submerged in a fluid.
(fluid can be liquid or gas)
Fluid Dynamics - Conservation Laws
What is the continuity equation?
ṁ = ρAv = ρQ
Equation of conservation of mass when applied to fluid flow
Fluid Dynamics - Fluid Energy
What is the pressure energy (Ep) of a fluid?
Energy in a fluid determined by pressure.
Higher pressure means higher energy, lower pressure means lower energy.
Ep = P/ρ
Fluid Dynamics - Fluid Energy
Pressure head (formula)
hp = Ep/g
or
= P/ρg
Fluid Dynamics - Fluid Energy
What is specific kinetic energy? (definition and formula)
The kinetic energy of a fluid evaluated per unit mass.
Ev = v^2 / 2
Fluid Dynamics - Fluid Energy
Velocity head (formula)
hv = Ev/g
or
= v^2/2g
Fluid Dynamics - Fluid Energy
What is specific potential energy? (definition and formula)
The potential energy of a fluid evaluated per unit mass.
Ez = zg
Fluid Dynamics - Fluid Energy
Elevation head (formula)
hz = Ez / g
or
= z
Fluid Dynamics - Hydraulic Grade Line
What is the hydraulic grade line (HGL)?
The graph of the pressure head, plotted as a position along the pipeline.
Fluid Dynamics - Energy Line
What is the energy grade line (EGL)?
The graph of the total energy along a length of pipe.
EGL = GHL + v^2/2g (velocity head)
Fluid Dynamics - Flow of a Real Fluid
formula for head loss due to friction (hf)
hf = (p1 - p2) / γ
