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| When do we use the integral approach? (Not differential) |
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| When we only want the gross behavior of the device, not the detailed behavior of the flow |
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| When do we use the differential form to solve a fluid mechanics problem? |
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| When we want to determine the detailed behavior of the flow |
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| Explain the continuum assumption |
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Fluid is approximated as a continous media (ignores molecular composition). Fluid properties are then defined at each 'point' in time.
We define the point by creating a control volume that looks like a point on a macroscopic level, yet is large compared to the molecules |
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| scalar quantity that acts normal to a surface. Force/area |
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| local thermodynamic pressure in a moving fluid: or the pressure at a nominated point in a fluid (wikipedia) |
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| Define Dynamic pressure, q |
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Kinetic energy per unit volume:
q = ρu²/2 (pascals) |
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(static pressure, p + dynamic pressure, q)
-represents the total energy available in flow:
p0 = p +q |
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| point in flow where velocity is zero |
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Dimensionless pressure relative to reference value
Cp =(p - p∞)/[(1/2) ρ∞*u∞2 ] |
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| Measures the 'stickiness' of the molecules and their resistance to motion |
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the Dynamic viscosity, µ, over pressure, ρ
µ/ρ |
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| No slip condition (in relation to viscosity) |
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| FLuid molecules in contact with a solid surface have the same mean velocity of that surface |
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| Nearly parallel layers sliding over one another |
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| Complex fluid motion. Characterized by a range of eddy like motions, bounded in size by width of flow at upper end and viscosity at lower end |
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Relates the surface integral of the curl of a vector field to the line integral of the vector field around a boundary curve.
The integral of the curl of the velocity u over a surface dA is equal to the line integral of u integrated over ds (tangent to the bounding curve) |
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also known as the divergence theorum...
The divergence of u integrated over a volume bounded by a surface A is equal to the vector u integrated over the area. |
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- Pathline
- Streamline
- Streakline
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| A line traced out by a single fluid element |
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| A line of fluid elements that all pass through a common point in space |
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| A line drawn in flow such that the tangents to the line are parallel to the local velocity vector at that instance in time |
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| Track fluid particle as it moves trough space |
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| Identify a volume in space and time (control volume) and keep track of fluid in that fixed volume |
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The study of fluids at rest and in stable equilibrium
Note: A fluid cannot stay at rest under the presence of a shear force |
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| Describe how pressure works on a fluid in static equilibrium: |
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| If we look at an infinitesimally small cubic fluid element, a stable equilibrium demands that the pressure on any side must be equal, since the fluid would move in the direction of the resulting force otherwise. |
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| Pressure exerted in a confined incompressible fluid is transmitted equally in all directions throughout the fluid such that the initial pressure ratio remains the same |
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| Explain the Hydraulic Press |
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In a hydraulic press, we have a two froces and two areas. The forces come from the force on the plunger and the weight of the ram. The areas correspond to the ram and plunger. Thus, the force/area ratios are equal for each element.
Fplunger/Aplunger=Wram/Aram |
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Is the pressure exerted by a fluid at equilibrium due to the force of gravity
Δp = -ρgΔh
or
δp/δV=-ρg |
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| Intuitive derivation of Hydrostatic Pressure |
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The force acting on an infinitesimally small cube of fluid at equilibrium is equal to the weight of the column of fluid above it
Δp = -ρgΔh |
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| Absolute pressure, Pabsolute= |
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| Pabsolute = Patm + Pgauge |
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| dx/ds = u (x and u in vector form) |
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| dx/dt = u(x(t),t) , u is in vector form |
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| Explain Archimedes principle |
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Any object wholly or partially submerged is buoyed up by a force equivalent to the weight of the water displaced
Buoyancy = weight of water displaced
Fbuoy= ρgV |
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| What constitutes a submerged body in stable equilibrium? |
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| Center of buoyancy is above center of gravity |
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| Hydrostatic forces (on surfaces) |
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The resultant force Fr of a static fluid due to the hydrostatic pressure distribution on the surface
abs(Fr) = (1/2)ρgh^2 |
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