Fluid Mechanics Flashcards by CASEY LORIMER

[Formula] Specific Weight (γ)

γ = pg –> (density)(gravity)

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[Formula] Force needed to move single-plate viscometer (F)

F = μvA/δ –> [(viscosity)(velocity)(area)] / thickness

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[Formula] Force (F)

F = ma –> (mass)(acceleration)

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[Formula] Mass (m)

m = pV –> (density)(volume)

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[Formula] Height change due to capillary action (h)

h = (4σcosβ) /γd = (4σcosβ) /pgd

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[Formula] Specific volume (υ)

υ = V/m –> volume/mass
υ = 1/p –> 1/density

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Fluid Statics - Hydrostatic Pressure

[Formula] Pressure (P) for a stationary, incompressible fluid

P = pgh –> (density)(gravity)(height)
or
P = γh –> (specific weight)(height)

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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.

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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.

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[Formula] Bernoulli Equation

P2/γ + v2^2/2g + z2 = P1/γ + v1^2/2g + z1

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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.

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Pressure

What are “absolute pressures?”

Pressures measured with respect to a ‘true zero pressure.’

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Pressure

What are “gage pressures?”

Pressure measured with respect to ‘atmospheric pressure.’

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Pressure

How are absolute and gage pressures related? (Formula)

P_absolute = P_atmospheric + P_gage

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Pressure

What is a ‘vacuum’ pressure measurement?

A pressure below atmospheric pressure (i.e., a negative gage pressure).

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Stress

Stress has a different symbol in “Materials” than in “Fluids.” What are those symbols?

τ for fluids

σ for materials

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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

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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

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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.

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Viscosity

What is the formula for viscosity of a Newtonian fluid?

τ = µ(dv/dy)

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Viscosity

What is the formula for viscosity of a non-Newtonian fluid?

τ = K(dv/dy)^n

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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