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ME 441 Quiz 2
| Question | Answer |
|---|---|
| what does the gradient physically represent? | the direction of maximum increase of the scalar field and the rate of change in that direction |
| what does divergence physically indicate in a fluid flow? | local net outflow or inflow of fluid |
| What does curl physically represent in fluid flow? | Local rotation or vorticity of the flow. |
| If the curl of a velocity field is zero everywhere, the flow is _______. | Irrotational |
| For incompressible flow, what must the divergence equal? | ∇⋅V=0 |
| Which operator is used for gradient, divergence, and curl? | The del operator: ∇ |
| T/F: The gradient operates on a vector field. | False (It operates on a scalar field.) |
| T/F: A flow with zero divergence is incompressible. | True |
| T/F: A flow with zero curl is irrotational. | True |
| T/F: Divergence measures rotation in a flow field. | False (It measures expansion/contraction.) |
| T/F: Curl is a vector quantity. | True |
| T/F: In 2-D flow, curl has only one non-zero component. | True (z-direction) |
| T/F: Incompressible flow can still be rotational. | True |
| The gradient of a scalar field gives the direction of __________ increase. | maximum |
| The divergence of a velocity field represents net __________ at a point. | outflow (or inflow) |
| For incompressible flow, ∇⋅𝑉= ____ | 0 |
| The curl of a velocity field is related to __________ in fluid mechanics. | vorticity (or rotation) |
| If ∇ × 𝑉 = 0, the flow is __________. | irrotational |
| The operator used to compute gradient, divergence, and curl is called the __________ operator. | del |
| How is divergence related to compressibility in a flow field? | Divergence measures the rate of volumetric expansion or contraction of a fluid. |
| Zero divergence → | incompressible flow |
| Nonzero divergence → | compressible flow |
| What does positive divergence indicate physically? | Local expansion of fluid (source-like behavior). |
| What does negative divergence indicate physically? | Local compression of fluid (sink-like behavior). |
| Can a compressible flow have zero divergence? | Yes — under special conditions (e.g., steady flow with constant density locally). |
| Can an incompressible flow be rotational? | Yes — incompressibility and rotation are independent properties. |
| What conservation law links divergence to compressibility? | Conservation of mass (continuity equation). |
| T/F: If a flow is incompressible, the divergence of velocity must be zero. | True |
| T/F: If the divergence of velocity is zero, the flow must be incompressible. | False (Only guaranteed if density is constant.) |
| T/F: Positive divergence corresponds to local fluid compression. | False (Positive divergence = expansion.) |
| T/F: Compressible flow always has nonzero divergence. | False |
| T/F: Divergence represents the net flux of velocity out of a control volume. | True |
| In incompressible flow, the divergence of velocity is equal to __________. | zero |
| Divergence measures the rate of __________ of a fluid element. | volumetric expansion (or contraction) |
| A flow with negative divergence is locally undergoing __________. | compression |
| The continuity equation expresses conservation of __________. | mass |
| Compressibility refers to the ability of a fluid to change its __________. | density |
| Divergence of velocity represents: | volumetric expansion or compression of a fluid element |
| incompressible flow requires: | zero divergence |
| How do you find the equation of a streamline from velocity components 𝑢(𝑥,𝑦) and 𝑣(𝑥,𝑦)? | Use the streamline slope relation: 𝑑𝑦/𝑑𝑥 = 𝑣/𝑢 Then integrate to obtain the streamline equation. |
| What is the defining property of a streamline? | A streamline is a curve that is everywhere tangent to the velocity vector. |
| What is the stream function 𝜓(𝑥,𝑦)? | A scalar function whose constant values represent streamlines. |
| T/F: The stream function is only defined for 2-D flows. | True |
| What does the constant 𝜓=𝐶 physically represent? | A specific streamline; different constants correspond to different streamlines. |
| In incompressible flow, the stream function automatically satisfies __________. | continuity (mass conservation) |
| What mistake do students often make when finding streamlines? | Forgetting to include the integration function f(x) or g(y). |
| Why is there a negative sign in the equation for 𝑣? | It ensures that the stream function automatically satisfies continuity for incompressible flow: ∂𝑢/∂𝑥 +∂𝑣/∂𝑦 =0 |
| T/F: The stream function formulation automatically satisfies conservation of mass for incompressible flow. | True |
| If both velocity components are derived from a stream function, what must the flow be? | Incompressible (2-D). |
| T/F: A stream function can exist for compressible flow. | False (standard stream function applies to incompressible 2-D flow) |
| If 𝜓 = constant, what does that represent? | A streamline. |
| T/F: A velocity potential can exist in rotational flow. | False |
| The velocity potential is only defined for __________ flows. | irrotational |
| How are streamlines and equipotential lines related? | They are perpendicular everywhere in potential flow. |
| How is irrotational flow related to vorticity? | Irrotational flow has zero vorticity everywhere. |
| Irrotational flow means the fluid particles move in straight lines. | False (They can curve but still not rotate.) |
| When do you use the irrotational flow assumption? | Viscous effects are negligible Flow is outside boundary layers and wakes Flow is away from solid surfaces Flow is at low to moderate angles of attack |
| Why is irrotational flow useful in aerodynamics? | Because it allows: Use of potential flow theory Superposition of elementary flows Analytical solutions for velocity, pressure, and lift |
| T/F: Irrotational flow implies incompressible flow. | False (They are independent assumptions.) |
| Can real flows ever be irrotational? | Yes — approximately, in regions outside boundary layers where viscous effects are small. |
| Irrotational flow is commonly assumed in __________ flow analysis. | potential |
| What is vorticity? | Vorticity is a vector that measures the local rotation (spin) of fluid particles in a flow. |
| If vorticity is zero everywhere, the flow is __________. | irrotational |
| What does positive vorticity indicate physically? | Fluid particles are rotating counterclockwise (right-hand rule). |
| Where does vorticity come from in real flows? | Vorticity is generated by viscous effects, primarily: No-slip condition at solid surfaces Boundary layers Flow separation and wakes |
| T/F: Inviscid (non-viscous) flow can generate vorticity. | False (Inviscid flow cannot create vorticity internally.) |
| T/F: Can vorticity exist away from solid surfaces? | Yes — once generated at walls, vorticity can be convected into the flow (e.g., wakes). |
| Vorticity is twice the local __________ of a fluid element. | angular velocity |
| How is vorticity related to circulation? | Circulation is the integral of vorticity over an area (Stokes’ theorem). |
| How does a Pitot probe work? | A Pitot probe measures fluid velocity by converting the kinetic energy of the flow into pressure at a stagnation point. |
| What pressure does a Pitot probe measure? | The stagnation (total) pressure, where the flow velocity is reduced to zero. |
| At the opening of a Pitot probe, the flow velocity is __________. | zero (stagnation point) |
| What two pressures are needed to calculate velocity using a Pitot probe? | Stagnation pressure 𝑝(0) Static pressure 𝑝 |
| T/F: A Pitot probe directly measures velocity. | False (It measures pressure; velocity is calculated.) |
| Why must the flow be incompressible to use the simple Pitot equation? | Because Bernoulli’s equation assumes constant density. |
| What correction is required at higher Mach numbers? | Compressible flow (isentropic) relations must be used instead of incompressible Bernoulli. |
| T/F: A Pitot-static probe measures both stagnation and static pressure. | True |
| Where is the static pressure typically measured on a Pitot-static probe? | Through side ports aligned parallel to the flow, unaffected by stagnation. |
| A Pitot probe relies on the __________ principle. | conservation of energy (Bernoulli) |
| What is the pressure coefficient? | The pressure coefficient is a dimensionless number that compares the local pressure to the freestream dynamic pressure |
| What does 𝐶𝑝 = 1 mean? | corresponds to a stagnation point, where the local velocity is zero. |
| What does 𝐶𝑝 = 0 mean? | means the local pressure equals the freestream pressure, so the local velocity equals the freestream velocity. |
| At a stagnation point, the velocity is __________ and 𝐶𝑝 =___. | zero, 1 |
| What does a negative pressure coefficient indicate? | The local flow velocity is greater than the freestream velocity (suction). |
| T/F: A large negative 𝐶𝑝 corresponds to high lift contribution. | True |
| Why is the pressure coefficient useful? | Because it: Is dimensionless Allows comparison between different flows Directly shows where lift is generated on an airfoil |
| If 𝐶𝑝 < 0, then the local velocity is __________ than the freestream velocity. | greater |
| What is an adverse pressure gradient? | An adverse pressure gradient occurs when pressure increases in the direction of the flow |
| Why is an adverse pressure gradient “adverse”? | Because increasing pressure opposes the flow, causing the fluid to lose kinetic energy and slow down. |
| An adverse pressure gradient causes the boundary-layer velocity to __________. | decrease (slow down) |
| How does an adverse pressure gradient lead to flow separation? | As the near-wall flow slows under an adverse pressure gradient, it can reverse direction, causing the boundary layer to detach from the surface (separation). |
| What is flow separation? | Flow separation is the point where the boundary layer breaks away from the surface and the wall shear stress goes to zero or becomes negative. |
| T/F: Flow separation occurs when the pressure decreases in the flow direction. | False |
| How does flow separation affect lift? | Separation reduces suction on the upper surface, causing lift to decrease sharply. |
| What is stall? | Stall is the condition where large-scale separation occurs on the airfoil, resulting in a sudden loss of lift. |
| Stall is typically caused by a __________ adverse pressure gradient at high angle of attack. | strong |
| Why does increasing angle of attack promote separation? | Higher angle of attack increases pressure recovery on the upper surface, creating a stronger adverse pressure gradient. |
| Which boundary layer type is more resistant to separation? | A turbulent boundary layer, because it has more momentum near the wall. |
| What is a laminar boundary layer? | A laminar boundary layer has smooth, orderly flow with fluid particles moving in parallel layers and little mixing. |
| What is a turbulent boundary layer? | A turbulent boundary layer has chaotic, fluctuating motion with strong mixing between fluid layers. |
| What is the main physical difference between laminar and turbulent boundary layers? | Turbulent boundary layers have higher momentum near the wall due to mixing, while laminar boundary layers do not. |
| Compared to laminar flow, turbulent boundary layers have __________ skin-friction drag. | higher |
| Which boundary layer is more resistant to an adverse pressure gradient? | A turbulent boundary layer. |
| Why does a turbulent boundary layer resist separation better? | Because mixing brings high-momentum fluid toward the wall, allowing the flow to overcome an adverse pressure gradient. |
| How does a laminar boundary layer affect stall? | Laminar boundary layers separate earlier, leading to earlier stall at lower angles of attack. |
| How does a turbulent boundary layer affect stall? | Turbulent boundary layers delay separation, allowing the airfoil to reach a higher stall angle of attack. |
| T/F: Turbulent boundary layers always improve aerodynamic performance. | False (They delay stall but increase drag.) |
| Why do some airfoils intentionally trip the boundary layer to turbulence? | To delay separation and stall, especially at low Reynolds numbers. |
| Laminar flow has lower drag but __________ stall resistance. | poorer (lower) |
| What is profile drag? | Profile drag is the drag associated with an airfoil’s shape and surface, excluding induced drag. |
| What are the two types of drag that make up profile drag? | Skin-friction drag Pressure (form) drag |
| Profile drag = __________ drag + __________ drag. | skin-friction, pressure (form) |
| What is skin-friction drag? | Drag caused by viscous shear stresses between the fluid and the airfoil surface. |
| What is pressure (form) drag? | Drag caused by flow separation, which creates a pressure difference between the front and rear of the airfoil. |
| Which type of profile drag is directly related to boundary-layer behavior? | Pressure (form) drag. |
| T/F: Skin-friction drag exists even if the flow does not separate. | True |
| T/F: Pressure drag is present even in fully attached flow. | False |
| Which boundary layer type increases skin-friction drag? | Turbulent boundary layers. |
| Which drag component increases significantly during stall? | Pressure (form) drag. |
| Profile drag does __________ include induced drag. | not |
| What are the normal force 𝑁 and axial force 𝐴? | Normal force 𝑁: perpendicular to the airfoil chord Axial force 𝐴: parallel to the airfoil chord |
| Lift is primarily aligned __________ to the freestream, while drag is aligned __________ to the freestream. | perpendicular, parallel |
| Why do we need to transform 𝑁 and 𝐴 into 𝐿 and 𝐷? | Because lift and drag are defined relative to the freestream direction, not the airfoil chord. |
| At small angles of attack, lift is approximately equal to the normal force. | True |
| Normal and axial forces are defined relative to the __________ of the airfoil. | chord line |
| Which force contributes most to drag at small angles of attack? | The axial force. |
| How are lift and drag calculated from the pressure coefficient? | By integrating the pressure coefficient distribution over the airfoil surface to obtain forces, then resolving them into lift and drag. |
| What force does the pressure coefficient directly represent? | The pressure (normal) force acting on the airfoil surface. |
| Why does pressure primarily contribute to lift rather than drag? | Because pressure acts normal to the surface, and for attached flow most of that force is perpendicular to the freestream. |
| Pressure coefficient integration directly gives the __________ force. | normal |
| What does the area between the upper and lower 𝐶𝑝 curves represent? | The lift coefficient. |
| How is drag obtained from the pressure coefficient? | By integrating the streamwise component of pressure forces over the surface; this contribution is called pressure (form) drag. |
| T/F: Pressure coefficient integration accounts for skin-friction drag. | False (Skin-friction drag comes from shear stress, not pressure.) |
| Under what condition does pressure drag become significant? | When flow separation occurs (e.g., near stall). |
| total drag equals pressure drag plus __________ drag. | skin-friction |
| If the upper-surface 𝐶𝑝 is much more negative than the lower-surface 𝐶𝑝, what happens to lift? | Lift increases. |
| What is the center of pressure (CP)? | The center of pressure is the point along the chord where the resultant aerodynamic force (lift + drag) effectively acts, producing zero net moment about that point. |
| How does the center of pressure behave as angle of attack changes? | The center of pressure moves along the chord as angle of attack changes. |
| The center of pressure is the point where the __________ is zero. | moment |
| What is the aerodynamic center (AC)? | The aerodynamic center is the point along the chord where the pitching moment is independent of angle of attack. |
| T/F: The aerodynamic center moves with angle of attack. | False |
| Why is the aerodynamic center more useful than the center of pressure? | Because its moment is constant with angle of attack, making it ideal for stability and control analysis. |
| T/F: At zero lift, the center of pressure is undefined. | True (Because lift appears in the denominator.) |
| Which point is commonly used in aircraft stability analysis? | The aerodynamic center. |
| For cambered airfoils, the pitching moment about the aerodynamic center is usually __________. | nonzero (typically negative) |
| Center of Pressure: | The point where the resultant aerodynamic force acts and the net moment is zero. |
| Aerodynamic Center: | The point where the pitching moment does not change with angle of attack, located near the quarter-chord. |
| The center of pressure is undefined when __________ equals zero. | lift |
| The center of pressure location is constant with angle of attack. | False (It generally moves as angle of attack changes.) |
| Why does the center of pressure move with angle of attack? | Because the pressure distribution changes, altering the moment balance along the chord. |
| Which reference point is most commonly used to calculate 𝑥𝑐𝑝? | The leading edge or the quarter-chord. |
| At zero lift, the center of pressure is __________. | undefined |
| Which is preferred for stability analysis: center of pressure or aerodynamic center? | Aerodynamic center, because its moment is independent of angle of attack. |
| What is a lift/drag coefficient chart (airfoil polar)? | A plot that shows how aerodynamic coefficients vary with angle of attack or with each other for a given airfoil and Reynolds number. |
| What are the most common axes you will see on these charts? | CL vs angle of attack 𝛼 𝐶𝐷 vs 𝐶𝐿 (drag polar) 𝐶𝑀 vs angle of attack 𝛼 |
| Lift coefficient 𝐶𝐿 is usually plotted on the __________ axis. | vertical (y) |
| How do you read the lift coefficient at a given angle of attack? | 1. Go to the specified angle of attack on the x-axis 2. Move vertically to the curve 3. Read the corresponding 𝐶𝐿 value on the y-axis |
| How do you identify stall from a 𝐶𝐿 vs 𝛼 plot? | Stall occurs at the maximum 𝐶𝐿, where the curve stops increasing and begins to drop. |
| What does the slope of the linear portion of the 𝐶𝐿 vs 𝛼 curve represent? | The lift-curve slope |
| How do you read drag coefficient from a drag polar (𝐶𝐷 vs 𝐶𝐿)? | 1. Find the desired 𝐶𝐿 2. Move horizontally to the curve 3. Read 𝐶𝐷 on the x-axis |
| The minimum drag coefficient corresponds to the __________ point on a drag polar. | lowest 𝐶𝐷 |
| What does the lowest point on a 𝐶𝐷 vs 𝐶𝐿 curve represent? | The minimum profile drag condition. |
| How do Reynolds numbers appear on lift/drag charts? | Each curve corresponds to a different Reynolds number, often labeled or color-coded. |
| T/F: Lift and drag coefficients are independent of Reynolds number. | False |
| Why must you use the correct Reynolds number curve? | Because 𝐶𝐿, 𝐶𝐷, and stall behavior change significantly with Reynolds number. |
| What does a negative 𝐶𝑀 on the chart indicate? | A nose-down pitching moment. |
| For a symmetric airfoil, 𝐶𝐿 = 0 occurs at approximately __________ angle of attack. | zero degrees |
Created by:
mccurdyo