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WorksheetsQuality Assessment 1 Gas Dynamics
Total questions: 35
Worksheet time: 18mins
What is the modulus of elasticity (K) in terms of compressibility (β)?
Bulk modulus K = 1/β
Bulk modulus K = β
K = β × V
K = β/ρ
What is the expression for Mach angle μ?
μ = sin⁻¹(1/M)
μ = cos⁻¹(1/M)
μ = tan⁻¹(1/M)
μ = M × 90°
How does Mach cone angle vary with Mach number?
Mach cone angle decreases as Mach number increases
Mach cone angle increases as Mach number increases
Both remain constant
No relation exists
What is the expression for change in entropy of an ideal gas in terms of temperature and volume?
Δs = Cv ln(T₂/T₁) + R ln(ρ₁/ρ₂)
Δs = Cp ln(T₂/T₁) + R ln(p₂/p₁)
Δs = Cv ln(T₂/T₁) − R ln(V₂/V₁)
Δs = Cp ln(T₂/T₁) − R ln(p₂/p₁)
Which section of the nozzle accelerates flow from subsonic to sonic speed?
Converging section
Throat section
Diverging section
Exit section
Which section of the nozzle gives supersonic acceleration?
Diverging section
Converging section
Throat
Diffuser
What equations govern isentropic flow through a nozzle?
Continuity, momentum, and energy equations
Only continuity and momentum equations
Bernoulli’s equation only
Only energy equation
What happens when back pressure increases above the critical value?
Flow remains subsonic throughout
Flow becomes supersonic in the diverging section
Flow chokes at the throat
Flow accelerates to Mach 2 at throat
What is the simplified potential equation for small-disturbance subsonic compressible flow?
(1 − M∞²) φₓₓ + φyy = 0
φₓₓ + φyy = 0
φₓₓ − M∞² φyy = 0
φₓₓ − φyy = 0
What is the general differential form of the continuity equation for unsteady compressible flow?
∂ρ/∂t + ∇·(ρV) = 0
∂V/∂t + ∇·V = 0
∂ρ/∂t + ∇²ρ = 0
∂p/∂t + ∇·V = 0
What is the continuity equation for steady compressible flow?
∇·(ρV) = 0
∂ρ/∂t + ∇·(ρV) = 0
∇·V = 0
∂ρ/∂x = 0
What is the continuity equation in Cartesian coordinates (x, y, z) for compressible flow?
∂ρ/∂t + ∂(ρu)/∂x + ∂(ρv)/∂y + ∂(ρw)/∂z = 0
∂ρ/∂t + ∂u/∂x + ∂v/∂y + ∂w/∂z = 0
∂p/∂t + ∂u/∂x + ∂v/∂y + ∂w/∂z = 0
∂ρ/∂t + ∂²ρ/∂x² + ∂²ρ/∂y² + ∂²ρ/∂z² = 0
What does the term ∂ρ/∂t represent in the continuity equation, where ρ is density?
Local rate of change of density
Local rate of change of velocity
Convective rate of change of density
Local acceleration
What does the term ∂(ρu)/∂x + ∂(ρv)/∂y + ∂(ρw)/∂z represent in the continuity equation, where ρ is density?
Convective term
Local term
Temporal term
Stagnation term
What is the main conservation principle expressed by the continuity equation?
Conservation of mass
Conservation of momentum
Conservation of energy
Conservation of entropy
What is the integral form of the mass conservation equation for steady 1-D flow?
ρuA = constant
ρA = constant
uA = constant
ρu = constant
What is the differential form of the mass conservation equation for steady 1-D flow?
dρ/ρ + du/u + dA/A = 0
dρ + du + dA = 0
dρ/ρ + du + dA = 0
ρ du + u dρ = 0
What is the differential form of the momentum equation for steady 1-D flow with varying area?
dp + ρu du = 0
dp + du = 0
dp = 0
ρu du = 0
What is the integral form of the momentum equation when A₁ = A₂ and Fx = 0 (A = area, F = force)?
p + ρu² = constant
p + ½ρu² = constant
p + u² = constant
p − ½ρu² = constant
What is the energy equation for a steady 1-D adiabatic flow?
h₀₁ = h₀₂
h₁ = h₂
T₁ = T₂
p₁ = p₂
What is the total temperature expression in steady adiabatic flow with no shaft work?
CpT₀₁ = CpT₀₂
CpT₁ = CpT₂
CpT₀₁ + u₁²/2 = CpT₀₂ + u₂²/2
CpT = constant
How does pressure change in a diverging section for subsonic and supersonic flow?
Increases for subsonic, decreases for supersonic
Decreases for subsonic, increases for supersonic
Increases for both subsonic and supersonic flow
Decreases for both subsonic and supersonic flow
What is the relationship between pressure and velocity in a converging nozzle for subsonic flow?
Pressure and velocity are inversely proportional
Pressure decreases as velocity increases
Pressure remains constant regardless of velocity
Pressure increases as velocity increases
What is the significance of the Mach number in compressible flow?
It indicates the speed of flow relative to the speed of sound
It measures the density of the fluid
It represents the temperature of the fluid
It is a dimensionless number representing viscosity
What is the effect of compressibility on the flow of gases at high velocities?
It only affects the temperature of the gas
It becomes negligible at high velocities
It leads to a decrease in pressure only
It significantly affects the flow characteristics
What is the relationship between temperature and pressure in a compressible flow?
Temperature increases as pressure increases
Temperature decreases as pressure increases
Temperature remains constant regardless of pressure
Temperature and pressure are independent
What is the effect of a shock wave on the flow properties of a gas?
It increases temperature and pressure
It decreases temperature and pressure
It only affects velocity
It has no effect on temperature and pressure
What is the significance of the Reynolds number in fluid dynamics?
It indicates the flow regime (laminar or turbulent)
It measures the density of the fluid
It represents the viscosity of the fluid
It is a dimensionless number representing temperature
What is the relationship between the speed of sound and temperature in a gas?
Speed of sound decreases with temperature
Speed of sound is independent of temperature
Speed of sound is directly proportional to pressure
Speed of sound increases with temperature
What is the effect of increasing the area of a nozzle on the flow velocity for subsonic flow?
Velocity increases
Velocity decreases
Velocity remains constant
Velocity becomes supersonic
What does the term ∂p/∂t represent in fluid dynamics?
Local rate of change of pressure
Local rate of change of density
Convective rate of change of pressure
Local acceleration of pressure
What is the relationship between the speed of sound and the molecular weight of a gas?
Speed of sound increases with molecular weight
Speed of sound decreases with molecular weight
Speed of sound is directly proportional to temperature and inversely proportional to molecular weight
Speed of sound is independent of molecular weight
What is the effect of compressibility on the flow of gases at high velocities?
It increases the velocity of the gas
It only affects the density of the gas
Compressibility has no effect
It leads to shock waves and changes in flow characteristics
What is the primary factor that determines the speed of sound in a gas?
Molecular weight of the gas
Pressure of the gas
Temperature of the gas
Density of the gas
What is the significance of the critical Mach number in compressible flow?
It indicates the transition from subsonic to supersonic flow
It is the maximum speed of sound in a medium
It represents the minimum pressure in a flow
It has no significance in fluid dynamics
