Fundamentals of Aerodynamics
6th Edition
ISBN: 9781259129919
Author: John D. Anderson Jr.
Publisher: McGraw-Hill Education
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Chapter 2, Problem 2.3P
Consider a velocity field where the x and y components of velocity are given by
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A pressurized tank of water has a 10-cm-diameter orifice at the bottom, where water discharges to the atmosphere. The water level is
2.5 m above the outlet. The tank air pressure above the water level is 250 kPa (absolute), while the atmospheric pressure is 100 kPa.
Neglecting frictional effects, determine the initial discharge rate of water from the tank. (Round the final answer to three decimal
places.)
-Air
250 kPa
dcm
2.5 m
The initial discharge rate of water from the tank is determined to be 18.683
m³/s.
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A 3-m-high large tank is initially filled with water. The tank water surface is open to the atmosphere, and a sharp-edged 10-cm-diameter
orifice at the bottom drains to the atmosphere through a horizontal 80-m-long pipe. The total irreversible head loss of the system is
determined to be 1.500 m. In order to drain the tank faster, a pump is installed near the tank exit. Determine the pump head input
necessary to establish an average water speed of 6.5 m/s when the tank is full. Disregard the effect of the kinetic energy correction
factors. (Round the final answer to three decimal places.)
Water
3 m
10 cm
80 m
The required useful pump head is 1.200 m.
(30 minutes) Consider a converging-diverging nozzle, which is open to stagnant atmosphere
at the inlet and connected to an infinitely large low-pressure reservoir downstream at the
outlet (see the figure below). The ambient pressure (pa) is 1 bar, the throat cross section area
is 0.1 m². Imagine that the pressure in the low-pressure reservoir (p₁) can be changed to
regulate the flow in the nozzle.
Me
Pa=1 bar
A₁ =0.1 m²
Ae
Pv
Pe
Low pressure reservoir
a) It is known that when p₁
=
0.8 bar, the nozzle is choked and the flow in the converging-
diverging nozzle is subsonic. Find the exit cross-section area (Ae), the static pressure at
the exit (pe) and the Mach number at the exit (Me) for this case.
b) Determine the range of vacuum pressure (pv) for which there is a normal shock wave in
the diverging section of the nozzle.
c) Imagine that a pitot-tube is inserted at the exit of the nozzle. What would be the total
pressure reading when: (1) p₁ = 0.8 bar; (2) p, is adjusted such that the…
Chapter 2 Solutions
Fundamentals of Aerodynamics
Ch. 2 - Consider a body of arbitrary shape. If the...Ch. 2 - Consider an airfoil in a wind tunnel (i.e., a wing...Ch. 2 - Consider a velocity field where the x and y...Ch. 2 - Consider a velocity field where the x and y...Ch. 2 - Consider a velocity field where the radial and...Ch. 2 - Consider a velocity field where the x and y...Ch. 2 - The velocity field given in Problem 2.3 is called...Ch. 2 - The velocity field given in Problem 2.4 is called...Ch. 2 - Is the flow field given in Problem 2.5...Ch. 2 - Consider a flow field in polar coordinates, where...
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- 1. Five forces are applied to the solid prism shown in Figure 1. Note that the 30 lb forces are in the plane of the prism's surface and are not vertical. Also note that the end of the prism is not an equilateral triangle. a) Compute the magnitude of the couple moment of the force couple formed by the 30 lb forces. b) Replace all the forces with an equivalent resultant force and couple moment acting at point A, Rand G. Give your answers as Cartesian vectors. Figure 1: 6 in a) G b) R GA B 5 in 5 in 4 in 40 lb 4 in 40 lb A 50 lb 30 lb 5 in E 5 in Yarrow_forward4) Calculate the thrust reduction due to the existence of a shock wave at the exit of the rocket no: given below, compared to the no shock case. P=200kPa I M=1.4 MCI M = 1 T=mle A₂ = 3m²arrow_forward3. (30 minutes) Find the mass flow rate for the converging-diverging nozzle below. A₁=0.1 m² V₁ = 150 m/s P₁ = 100 kPa T₁ = 20°C M>1arrow_forward
- Q4. Derive the y-momentum equation for a thin laminar boundary layer using the general form of the y-momentum equation for two-dimensional and steady flow given below. до pu +pv- Əx до др მ dy ду +(x+7) ди дхarrow_forward1) Solve the problem using the superposition method. Check that your answer is correct.For steel, use a Poisson's ratio of 0.3.arrow_forward3. Consider a subsonic compressible flow in Cartesian coordinates where the perturbation velocity potential is given by: 20 $(x,y) = -2π e 1-M sin(2x) √1 - M² The free-stream properties are Vo。 = 200 m/s, p∞ = 150 kPa and T∞ = 250 K. po a. Compute the Mach number at the location (x, y) = (0.8, 0.2). b. Compute the pressure coefficient at the wall at the wall at (x, y) = (0.8,0) using both the = 2 2û | and the small perturbation approximation (Cp = -2). exact relation [Cp = M-1)] andarrow_forward
- Q2) (30 minutes) The pressure distribution over a curved surface is given below. Find an expression for the friction coefficient assuming there exists a turbulent boundary layer over the surface with a power law velocity profile as given in the figure. y P/Pmax 1.0 0.5- 0.25 - u = de y б → อ 0.3 1.0 ри 0 = PeUe de dx 8* = 1 - ри PeUe (1-0)ay 0 due -- Ue dx = dy 1 - Ue dy + น dy = (2 + H) = 1 Cf 2 - и Ue dy v2 + + gz = constant 2 Ρarrow_forwardQ3. A piecewise linear function approximates the velocity profile in an incompressible boundary layer flow over a flat plate, as shown in the figure below. Under the assumption of a constant edge velocity (U) in the streamwise direction (i.e., the x direction), calculate the skin friction coefficient as a function of the Reynolds number. وانه δ со 2/3 Ve Ve u 1- 8* = √² (1 - Du₂) dy pu ри PeUe น 9 = √²* Du (1-7) dy de dx 0 PeUe δ + 0 due (2+0²) = 12/24 Ue dx 8 ≤ 100arrow_forward4. The streamwise velocity component (u) for a laminar boundary layer is given by: u = Ue 8 = b√√x where b is a constant and U is the edge velocity. Obtain an expression for the vertical velocity component (v) at the edge of the boundary layer.arrow_forward
- Please Solve Q1&Q2&Q3arrow_forwardFind the equations of motion of the double elastic pendulum below using Lagrange's equations.arrow_forwardProblem 2. (35 pts) Consider the Atwood machine with rope length / depicted below. The spring with constant k is initially unstretched. Find the equations of motion using Lagrange multipliers by using the configuration coordinates y₁, y2, and y3. Y₁ m1 lllllllllllllllll k Уз Y2 m2arrow_forward
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