TP2 - Fluid Mechanics Flashcards
What’s kinetic and dynamic viscosity?
Dynamic Viscosity (μ): Measure of internal resistance
Kinematic viscosity:
Ratio of dynamic viscosity to density
v = 𝜇 / 𝜌
What’s an open channel flow?
Fluid flow which experiences a liquid-gas boundary layer
How can open channel flow be described?
Flow can be uniform or varied (non-uniform)
UF - uniform flow
GVF - gradually varied flow
RVF - rapidly varied flow
How does the velocity profile change along the length of a channel with steady, uniform flow?
It does not change.
What is a prismatic channel?
A channel with:
- a constant cross-sectional area
- constant surface roughness
- a constant clope
What are the (2) forces balanced in an open channel?
Gravitational = Drag
Forces acting to speed the fluid = forces acting to slow the fluid.
Involved with open channel equations, what do the following symbols represent?
W α 𝜏₀ L HL y A P Rₕ C f
W - Weight of water (N)
α - Angle of slope (°)
τ₀ - Shear stress (Pa)
L - Length of bed (m)
HL - change in elevation across length m(m)
y - depth of liquid
A - CSA
P - wetted perimeter
Rₕ - hydraulic radius
C - Chezy coefficient
f - fanning friction factor
What is the force balance for an open channel?
Gravitational = Drag
𝑊 sin 𝛼 = 𝜏₀ × 𝑤𝑒𝑡𝑡𝑒𝑑 𝑎𝑟𝑒𝑎
𝑊 sin 𝛼 = 𝜏₀ × 𝐿𝑃
(since sin 𝛼 ≈ 𝑆 = 𝐻𝐿/𝐿)
𝑨𝝆𝒈 𝑯𝑳/𝑳=𝝉₀ 𝑷
How is hydraulic radius calculated?
Rh = cross-sectional area / wetted perimeter
= A / P
(Rh for a half-full pipe = D/4)
What is the Chezy equation?
𝒖=√((𝟖/𝒇)*𝑹_𝑯 𝒈𝑺)
Where:
f - fanning friction factor
Rh - hydraulic radius
S - slope
It describes the mean flow velocity of turbulent open channel flow.
What is the empirical Manning equation?
C = (1/n)*Rh^1/6
Where:
C - Chezy coefficient
n - manning coefficient
Rh - hydraulic radius
What is the equation combining the Chezy and Manning equations?
u = (1/n)Rh^(2/3)S^(1/2)
which calculates velocity.
Since flowrate, Q = Au,
Q = (1/n)A*Rh^(2/3)S^(1/2)
At what Reynolds number does an open channel system flow change from laminar to turbulent?
When Re is approximately 600.
What’s a compressible fluid?
A fluid whose volume is dependent on its temperature and pressure.
It’s density can change.
What does isentropic mean?
Constant entropy
What’s choked flow?
Choked flow is a limiting condition where the mass flow will not increase with a further decrease in the downstream pressure environment for a fixed upstream pressure and temperature.
Choked flow is a compressible flow effect. The parameter that becomes “choked” or “limited” is the fluid velocity.
What is the simplified energy balance equation?
udu + VdP = 0
Assumptions:
- Fully turbulent flow → Uniform Velocity Profile (α = 1)
- Horizontal Flow (dz = 0)
- Ideal Gas
- No external work or heat transfer to the surroundings
- Frictional losses are neglected
What is sonic velocity?
The velocity of sound in that fluid
Are velocity and mass flowrate for isothermal and adiabatic/isentropic flow systems calculated in the same way?
No.
They are quite different and adiabatic/isentropic flow consider the ratio of Cp to Cv too (gamma)
What’s a Laval nozzle?
A converging-diverging nozzle used to expand gases when P drop is large, with minimal energy loss (reversible process).
(Typically non-isothermal processes)
What is transonic flow?
where air flows above, at, and below the speed of sound at the same time at different points on an object.
For example, the air on a wing flows faster, so that air could be supersonic while the air flowing over the body of an airplane could be subsonic
How is sonic velocity calculated for an ideal gas under adiabatic conditions?
u.w = (γRT/M)¹/²
When Wc = P₂/P₁, the velocity of the fluid is known as the sonic velocity.
What’s the Mach number, Ma?
The ratio of the fluid velocity, u, to the sonic velocity, uw.
Ma = u / uw
What is critical flow?
When fluid velocity, u, is equal to sonic velocity, uw, and so the Mach number is 1.
What is critical, supersonic and subsonic flow?
Critical:
velocity = sonic velocity (u = uw) therefore Ma = 1
Supersonic:
u > uw therefore Ma > 1
Subsonic:
u < uw therefore Ma < 1
What do de Laval nozzles do?
They can accelerate hot, pressurised gas to a supersonic speed and, upon expansion, shape the exhaust flow so that the heat energy propelling the fluid flow is ‘maximally’ converted into directed kinetic energy.
What are the key concepts and assumptions made for when using Laval nozzles?
- Non-Isothermal. High flow rates means no time for temperature equilibration (a temperature gradient exists along the nozzle)
- Isentropic. No shock waves should be propagating within the nozzle
- Fully turbulent flow → Uniform Velocity Profile (α = 1)
- Horizontal Flow (dz = 0)
- Ideal Gas
- No external work or heat transfer to the surroundings
- Frictional losses are neglected
How is minimum throat area for a Laval nozzle calculated?
(G²(V₁/P₁)((γ-1)/2γ)*(Wc^(-2/γ)/(1-Wc^(γ-1/γ)))^¹/²
What’s choked flow?
When a flowing fluid at a given pressure and temperature passes through a constriction (such as the throat of a convergent-divergent nozzle or a valve in a pipe) into a lower pressure environment the fluid velocity increases.
At initially subsonic upstream conditions, the conservation of mass principle requires the fluid velocity to increase as it flows through the smaller cross-sectional area of the constriction.
At the same time, the Venturi effect causes the static pressure, and therefore the density, to decrease at the constriction.
Choked flow is a limiting condition where the mass flow will not increase with a further decrease in the downstream pressure environment for a fixed upstream pressure and temperature.
What’s the simplified energy balance when designing pipe systems?
udu + VdP + dF = 0
Assumptions 1. Fully turbulent flow → Uniform Velocity Profile (α = 1) 2. Horizontal Flow (dz = 0) 3. Ideal Gas 4. No external work or heat transfer to the surroundings
What are the limiting factors when designing piping systems?
Erosion (e.g. entrained dust/liquid) and stress on pipe wall → maximum safe velocity
Compressors are expensive → Maximum allowable pressure drop
Maximum velocity (and flowrate) (critical flow at exit)
How can the critical pressure ratio be solved / how must the Pw equation be solved?
This cannot be solved analytically – it needs to be solved one of two ways:
- Iteratively (not preferable)
- Using a graph someone else has made solving this equation already
What is the general energy balance for compressible flow?
1/a * udu + gdz + vdP + 𝛿Ws + 𝛿F = 0
