Equations - Meaning and Units

Question 1

What is the equation/ units for mass flow rate?

Answer 1

ρvA=C

Units: kg/s

Question 2

What is the equation/ units for volume flow rate?

Answer 2

v*A=C

Units: m^3/s

Question 3

What is the units for the outcome of Bernoulli’s equation?

Answer 3

Total pressure - Pascals

Question 4

What is each component of Bernoulli’s equation called? what does each mean?

Answer 4

ghρ = Potential pressure (due to change in height)
p = static pressure
0.5*ρ*v^2 = Dynamic Pressure (due to particles being bright to rest in airflow)
P = Total Pressure

Question 5

What is each component of Bernoulli’s equation for total head?

Answer 5

h = (natural) head
v^2/(2g) = Dynamic head
p/(gρ) = Static head
H = Total head

Question 6

What are the conditions to use Bernoulli’s equation?

Answer 6

Incompressibility
Ideal fluid
Steady state
Follow streamlines

Question 7

What is the Equation for calculating total pressure when you have static and dynamic pressure?

Answer 7

Static pressure + Dynamic pressure

Question 8

What is the state equation of gas? Derived from the ideal gas law?

Answer 8

p1/(ρ1T1) = p2/(ρ2T2)

(p1V1)/T1 = (p2V2)/T2

Question 9

What is the first law of thermodynamics? (energy conservation). What does each symbol represent?

Answer 9

Q = E + W

Q = Heat transferred to/from the system
E = Change in internal energy of the gas
W = Work done to/by the system

Question 10

What equations (2) can be derived from the ideal gas law if it undergoes an isothermal state change?

Answer 10

p1V1 = p2V2

p1/ρ1 = p2/ρ2

Question 11

What equations can be derived from the ideal gas law if a gas undergoes an isobaric state change?

Answer 11

V1/T1 = V2/T2

ρ1T1 = ρ2T2

Question 12

What equations can be derived from the ideal gas law is a gas undergoes an isochoric/ isovolumetric state change?

Answer 12

p1/T1 = P2/T2

p1/P2 = T1/T2

Question 13

What equations (3) can be derived from the ideal gas law/ first law of thermodynamics if a gas undergoes an adiabatic state change?

Answer 13

P1V1^γ = P2V2^γ

P1/ρ1^γ = P2/ρ2^γ

(P1^(γ-1))/T1^γ = (P2^(γ-1))/T2^γ

Question 14

What does each component of the shear stress equation mean? Units?

Answer 14

µ = Dynamic viscosity: Pa*s
∂u/∂y = Speed gradient in the y direction
τ = Shear stress

Question 15

What is the equation for Kinematic viscosity?

Answer 15

µ/ρ

Question 16

What is the equation for Reynolds Number? Units? What is its meaning? What is the meaning of l?

Answer 16

Re= ρvl/ µ
Dimensionless number used to classify the status of fluid flow

In a pipe it is the diameter (m), over a plate, it is the characteristic length (m)

Question 17

In a pipe, when is flow, turbulent, laminar or transition?

Answer 17

Laminar if Re<2000

Transition if 2000 4000

Question 18

Over a flat plate, when is a boundary layer flow laminar or turbulent?

Answer 18

Laminar if Re < 510^5
Transition if Re > 510^5 or Re < 510^6
Turbulent if Re > 510^6

Question 19

Describe the NACA naming convention?

Answer 19

1st number: percentage of max camber to chord
2nd number: position in 10ths of chord of max camber
3rd/4th number: percentage of max thickness to chord

Question 20

What is the formula for the Force due to circulation

Answer 20

F= ρvΓ

Question 21

What is Cl roughly equal to?

Answer 21

Cl = 2πα

Question 22

What is Cl roughly equal to for a non-symmetrical aerofoil?

Answer 22

Cl = Cl0 + 2kπα

Cl = kπ (α0 + α)

Question 23

How does the continuity equation change when looking at the speed of sound in air?

Answer 23

ρvA = (ρ + ∂ρ) * (v + ∂v) * A = C

Question 24

What is the equation for Mach number?

Answer 24

M = v/a

M = TAS/LSS

Question 25

What is the equation for fluidity?

Answer 25

1/µ