Questions and Answers of Fundamentals Of Aerodynamics

In the process of the space shuttle entering the earth’s atmosphere, the maximum stagnation point heating occurs at the trajectory point corre- sponding to the altitude of 68.9 km, where ρ∞ =
A group of affine airfoils is tested in a low-speed wind tunnel under the condition ofand the relationship between the minimum pressure coefficient and the relative thickness is as follows: Try to
There is a rectangular wing with aspect ratio λ of 3.5, its profile is NACA0006 airfoil, and it flies in a steady straight line at Ma∞ = 0.85 at the altitude of 12 km. Try to calculate the
The cross-section area distribution along the x-direction of the body axis of a thin wing-body assembly is given as where V is the volume of the combination, upper S left parenthesis x right upper S
There are two flat triangular wings with aspect ratio A = 3.0 and 1.0, flight Mach numbers are and a small angle of attack alpha.Try to calculate the lift coefficients of the two wings and the
As shown in the figure, there is a long thin wing-body assembly with pointed tips. The body of the wing-body connection area is a cylindrical section. Try to find the ratio of cylindrical section R
Try to find the ratio of the lift force of a slender cylindrical fuselage and triangular flat wing with small aspect ratio in the case of to the lift force of which at the angle of attack in the
There is a triangular-shaped wing with a leading edge sweep angle of 45° is now flying at speed of Try to consider how the leading edge characteristic of the wing change when flying at 5500 m and
A symmetrical double-cambered airfoil is placed in a supersonic flow, and the relative position of its focus (also its pressure center) is calculated by using the second-order approximate pressure
There is a wing with plane shape shown in figure, try to find the range of supersonic leading edge and subsonic trailing edge. Max
According to the linearized supersonic theory, the equation predicts that the plate decreases with increasing right? Does this mean that the drag itself decreases as increase? To answer this
The figure shows a combination of a slender cylindrical fuselage and a small aspect ratio triangular flat wing with a sweep Angle of 60°, When the fuselage angle of attack is zero and the wing
The figure shows that the incoming flow with velocityinfinityaround a two-dimensional cylinder with radius R along the y-axis (see figure). Find the maximum and minimum values of the y-direction
The airfoil shown in figure moves at the ratio of thickness and chord length is 0.1, and the maximum thickness takes place at 30% chord length behind leading edge. Use linearized theory to find(1)
A two-dimensional plate flies at altitude of 6 km andangle of attack is Try to find the pressure difference between the upper and the lower surface, using shock wave—expansion wave theory and
Calculate the pressure of upper and lower surfaces of a infinite wingspan thin plate in the free flow of Mach number is 2.6, at angle of attack of (a) = = 5 (b) = 15 (c) a == = 30 (use the form of
Assume the angle of attack of the wing in above question is zero, try to find the pressure at point B by using shock wave—expansion wave theory and linearized theory respectively.
An infinite wingspan wing with a symmetrical rhombus profile, as illus-trated in the attached figure, to move left in sea level air at Relative thickness use the theory of shock wave and expansion
Using the results of linearization theory, calculate lift and shock wave drag of infinite thin plate in the free flow of Mach number of 2.6 at angle of attack of (a) = 5 (b) = 5 (b) a 15 (c) =
Consider the flow pass a cylinder. Subsonic compressible flows on cylinder and sphere are similar in but differ in magnitude from them in Incompress-ible flow. In fact, because of the blunt shape of
For a given airfoil, Critical Mach number is 0.8. When find the minimum value of M = 0.8,
At a very low Mach number, the pressure coefficient at certain point of 2D airfoil is 0.5. What is the pressure coefficient at this point when the summation according to the linearization theory?
Suppose the formula satisfying the subsonic small disturbance linearization equation, with Try to write the differential equation of the streamline and solve the streamline equation by integral.
Consider a subsonic compressible flow in the Cartesian coordinate system, where the velocity potential is determined byIf the free flow properties are given by and properties at position (x, y) =
The pressure coefficient distribution at on the airfoil measured in the low speed wind tunnel is shown below. Based on these infor-mation, estimat that the Critical Mach number of the NACA0012
The theoretical lift coefficient for a symmetric thin airfoil in the Incom- pressible flow is The lift coefficient when is? CI = .
Please demonstrate the physical reason thatcan be written as Cp (Ma, , c, f) = C(0, B, c, Bf)
A civil aircraft uses a trapezoidal swept-back wing with Use the engineering calculation method to calculate the upper of the wing. = 8, = 2, = Xo
The of a non-twisted straight wing withunder a certain Reynolds number is shown in the figure. From the figure, it can be obtained that If other parameters remain the same, but λ is reduced to 5,
For a rectangular wing Try to calculate the induced drag and the ratio of induced drag to total lift when the aircraft is flying at sea level with = 6,1 = 12 m, wing load G/S = 900 N/m.
For a flat delta wing with try to use the engineering calculation method to find the values of =3, known C = 2, Loo
A curved airfoil, If this airfoil is placed on an elliptical wing with λ = 5 and no twist, try to find the aooo -4,C 2/rad.
Try to prove that if a horseshoe vortex line with a span length ofland a strength of the circulation of the wing root profile of the original wing is used to simulate the total lift of the
There is a monoplane with a weight of G=7.38× 104 N, the wing is an elliptical plane shape, the wingspan length is L = 15.23 m, and it is flying straight at the sea level with a speed of 90 m/s, try
An airplane with a weight of G = 14700 N, Cruising (Y = G)at h = 3000 m with airfoil non-twisted elliptical plane shape. Try to calculate V = 300 km/h, wing area S = 17 m, = 6.2, NACA23012
If the wing is replaced by a II-shaped horseshoe vortex line, the span length of the attached vortex is L, as shown in Fig. 6.6 of the exercises, try to prove(1) The downwash angle at position a
Given that the spanwise circulation distribution of a high aspect ratio wing is try to use the lifting-line theory to solve(1) Downwash speed (2) Downwash speed use integral T(z) r() = Fo[1 (?)]/
Assume that the spanwise circulation distribution of a straight wing with a high aspect ratio is parabolic, as shown in the figure. If the total lift is equal to the elliptical circulation
Given the sweep angle χ0 of the delta wing and the aspect ratio λ, try to prove Given the sweep angle χ0 of the delta wing and the aspect ratio λ, try to prove from the geometric relationship
There is a straight trapezoidal wing S = 35 m2, taper ratio and wingtip chord length find the aspect ratio λ of the wing. = 4.
Consider NACA 23012 airfoil. The average arc of the airfoil is given by Calculate (a) lift at zero angle of attack, (b) lift coefficient at (c) moment coefficient at quarter chord length, and (d)
The low-speed air flow flows through a thin symmetrical airfoil at a small angle of attack as shown in the fellow figure. Try to solve the fellow questions using the method of angle of attack
There is a curved airfoil withas shown in the fellow figure. Try to prove c = 1, yf = 8.28 (123-2x2+x) 8
There is a flat elliptical airfoil with as shown in the fellow figure. Try to apply the thickness problem of thin airfoil theory to calculate the lowest pressure strength coefficient at the
The airflow flows through a parabolic curved airfoil The vortices distributed on the bending plate are concentrated attwo points, and the vortex strength is normal respectively, as shown in the
A curved airfoil with c = 1 andwhere k is a constant and Try to calculate the yf = kx(x 1)(x2)
The arc equation of NACA2412 airfoil isAs shown in the fellow figure. Try to calculate according to thin airfoil theor - [ y = 1 (0.80x = x), 0 x 0.4 y = 0.0555 (0.20 +0.80x = x), 0.4 x 1.0
NACA2415 airfoil is used as the flat wing of a low-speed aircraft. What is the - f, xf and c?
The supersonic airflow with expands at a deflection angle of 15° at a sharp corner (see picture). Calculate and the angle of the front and rear Mach lines relative to the upstream flow direction.
The airfoil is in free flow, where andAt a certain point on the airfoil surface, the pressure is 50662.5 Pa. Assuming an isentropic flow, calculate the velocity at that point. P = 61,808.25 Pa, po =
Consider the air at a pressure of 20,265 Pa. Calculate the values ofand
Consider the isentropic flow through the nozzle of a supersonic wind tunnel. at the nozzle exit, calculate the exit temperature and density. To = 227C, Po = 1013250 Pa. If P = 1013250 Pa
Consider the isentropic flow on the airfoil. The free-flow condition isAt a certain point on the airfoil, the pressure is 3.6 × 104 N/m2. Calculate the density at this point. Too =
Calculate the ratio of kinetic energy to internal energy at a certain point in the airflow, where the Mach number is (a) Ma = 2 and (b) Ma = 20.
Considering the normal shock wave in the air, its upstream flow character-istics areCalculate the velocity, temperature, and pressure downstream of the shock wave. U1 = 680 m/s, T = 288 K, and pi =
If the 1/7 exponential law is used for the velocity profileProve that the displacement thickness and momentum loss thickness of the boundary layer are delta Therefore, for the flat, us || | = 96
Assume that the velocity distribution in the boundary layer of the flat plate (length L)iswhere δ is the thickness of the boundary layer. Try the momentum integral relational method to solve and
According to the exponential law of turbulence velocity distribution in the boundary layer Try to find the thickness of the turbulent boundary layer δ. us || = () and 0.185Re-
If the velocity distribution in the laminar boundary layer of a flat plate is a sinusoidal curve, Try to find the relationship between and u = us sin().
The velocity distribution in the laminar boundary layer of a flat plate is as follows: Try to find the relationship between the thick-ness of the boundary layer and the frictional resistance
For the laminar boundary layer on a two-dimensional curved surface with a radius of curvature of R, set the velocity distribution in the boundary layer asThe streamlines in the boundary layer have
If the velocity at the outer boundary of the boundary layer is is a constant. Try to prove that the corresponding pressure change isTherefore, m > 0 represents the forward pressure gradient, and
A flat plate with a length of 6 m and a width of 2 m is placed parallel and static in an air flow at a speed of 60 m/s at 40 °C. The critical Reynolds number of the transition from laminar flow to
An oil flow with a temperature of 20 °C and flows longi-tudinally around a thin flat plate with a width of 15 cm and a length of 50 cm at a speed of 0.6 m/s. Try to find the total frictional
A flat plate with a chord length L of 3.5 m,Try to estimate the thickness of the boundary layer at the rear edge of the slab (all laminar flow). ReL 105
If the velocity distribution functions of the boundary layer are and Try to calculate the displacement, momentum loss and energy loss thickness of the boundary layer. n Voo
If the velocity distribution functions of the boundary layer are and please calculate the displacement, momentum loss, and energy loss thickness of the boundary layer. 36 n Voo 8
The wing chord length of a certain aircraft is and it is flying at a speed of in the atmosphere with air pressure and temperature It is planned to be used in a wind tunnel for model tests. To
It is known that the venturi flow rate y is related to the flow rate difference the main pipe diameter the throat diameterand the fluid density and kinematic viscosity v.Try the theorem to
The shaft power N of the water pump is related to the torque M and the angular velocity of the pump shaft. Use the Rayleigh method to derive the expression of the shaft power.
Petroleum flows through a 15 m long horizontal pipeline. The power delivered to the flow is 1 hp. (a) If the flow is at the transition point of laminar flow, what is the appropriate pipe diameter?
As shown in the figure, the oil flows upward through the inclined pipe at a distance of The distance between Section 1 and Section 2 is 10 m. Assuming that the laminar flow is stable, (a) calculate
A flat plate with a length of 6 m and a width of 2 m is placed in a parallel and static air flow at a speed of 60 m/s at 40 °C, and the critical Reynolds number of the transition from laminar flow
Two concentric circular tubes with an outer diameter of and an inner diameter of rotate in the same direction at angular velocities Try to prove The velocity distribution between the two circular
The incompressible viscous flow of air between two infinitely long parallel plates with a distance h. Both parallel plates are stationary, but there is a constant pressure gradient in the flow
The figure shows that the two plates move in the opposite direction find the effect on each Tangential stress of a flat plate. V = 202
The relative density of the oil the viscosity and it flows through the annular pipe with and If the pressure drop per meter of pipe length is 196 Pa when the pipeline is placed horizontally, try
The gauge pressure of the oil in the cylinder the viscosity of the oil the diameter of the plunger the radial gap between the plunger and the sleeve the length of the sleeve Suppose that the
Given that the velocity of plane irrotational flow is velocity potential try to find the flow function and velocity field. =
Superposition point vortices and point sources with the center at the origin, and test that the resultant flow is a rotational flow. In this flow, the angle between the velocity and the polar radius
The flow function of incompressible fluid in plane flow istry to find its velocity potential. = Oxy+2x-
Try to prove that the incompressible fluid plane flowwhich satisfies the continuity equation, is a potential flow, and finds the velocity potential. = 2xy + x, Vy
For the flow around a circular cylinder, integrate the pressure on the cylinder surface to find the lift of the cylinder. The pressure coefficient on the cylinder is C, 1-2 sin 0 + = 1 - (2 si 2
Please give the Angle of the stationary point on the cylinder surface corresponding to the point vortex strength
A pipe system is placed on a horizontal plane. pipe diameters areMean flow rate at the inlet isStatic pressure (measured pressure) isWithout considering energy loss, try to find the horizontal force
Mass flowthe temperature is 400 °C, the pipe section size is 400 × 600 mm. The density of the air in standard state (0 °C, 101,325 Pa) is ρ = 1.29 kg/m3. Please calculate the average flow rate of
Find the flow rate of the fluid in a single width between two parallel plates. The velocity distribution is known aswhere y = 0 is the center line, y =±b is the position of the plate, and m is a
Given that an incompressible fluid is flowing in a plane, the velocity component in the y direction isTry to solve the velocity component in the x direction Uy u = y = 2x+2yux.
Let the following functions represent the three fractional velocities of the flow:Which case represents incompressible flow? (a) u = xyz, v=-yx (b) u = x+3zx, w = z + y
The velocity field of an incompressible fluid in steady motion iswhere a is a constant:(1) Line deformation rate, angular deformation rate;(2) Whether there is rotation in the flow field;(3)Whether
Fluid motion has partial velocityIs there rotation in the flow field? If there is no rotation, find the velocity potential function. u = v = x (x+ y+22)/2 y (x+y+22) 2 3/2 W = (x + y+22) 3/2
The velocity field of plane flow iswhere C is a constant, try to find the streamline equation. u = cy x+y CX v = x+ y
The following velocity fieldTry to find out: (1) the acceleration of point (1, 2, 3); (2) whether it is a multi-dimensional flow; (3) whether it is a steady flow or an unsteady flow; (4) whether it
The two-dimensional velocity field is made up ofAt that time, the calculation(a)the accelerations ax and ay, (b)the velocity component in the direction θ = 40°, i. Maximum velocity direction, and
The velocity field isandTry to calculate the circulation around a circular path with a radius of 5 m. u = y/(x + y)
The velocity component of the flow fieldCalculate the equation of streamline through the point (0, 5). = y/(x+ y) and v =
In Lagrange method, the following particle motion is characterized by (a,b, c) invariance. How to characterize the particle following in Euler’s method? Explain the difference between the following
The height of the Mariana Mountains in the Pacific Ocean is 11,034 m. At this height gamma Subscript s e a w t r Baseline equals 10520 normal upper N divided by m cubedgamma Subscript s e a w a t e r
As shown in the picture, two plates are filled with two kinds of unmixed liquids, the viscosity coefficient of which is liquid dynamic viscosity m 1 equals 0.14 Pa s comma 2 0.24 sm 1 equals 0.14 Pa
For a wide channel with a rectangular section, the flow velocity distribution iswhere γ is the bulk density of water, μ is the dynamic viscosity coefficient of water, y is the water depth, and h =

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