Thinking Like an Engineer: An Active Learning Approach (4th Edition)
4th Edition
ISBN: 9780134639673
Author: Elizabeth A. Stephan, David R. Bowman, William J. Park, Benjamin L. Sill, Matthew W. Ohland
Publisher: PEARSON
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Chapter 9, Problem 9ICA
It is proposed to create a set of dimensionless numbers used to describe the phenomena of reaching the escape velocity necessary to orbit the Earth. A set of names is proposed, based on famous astronauts:
- The Gagarin number, after Yuri Gagarin, a Russian astronaut and the first human to achieve escape velocity and orbit the Earth in outer space;
- The Valentina number, after Valentina Tereshkova, a Russian astronaut who was the first female to orbit the Earth;
- The Shepard number, after Alan Shepard, the first American to orbit the Earth; and
- The Ride number, after Sally Ride, the first American woman in space.
To begin the analysis, assume the following variables are important:
| g = Gravitational pull between planet and rocket | [=] meters per second squared [m/s2] |
| nr = Amount of rocket fuel | [=]moles [mol] |
| wp = Weight of planet | [=] pounds-force [lbf] |
| d = Diameter of planet | [=]miles [mi] |
| G = Newtonʼs gravitational constant | [=] newton meters squared per kilogram squared [N m2/kg2] |
| v = Velocity of rocket | [=] miles per hour [mph or mi/h] |
| η = Efficiency of the rocket engine | [=] unitless |
Determine a set of dimensionless groups using Rayleighʼs method.
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I am trying to plot an orbit in MATLAB. There is something wrong with my code because the final values I get are incorrect. The code is shown below. The correct values are in the image.
mu = 3.986*10^5; % Earth's gravitational parameter [km^3/s^2]
% Transforming orbital elements to cartesian coordinate system for LEOa_1 = 6782.99;e_1 = 0.000685539;inc_1 = 51.64;v_1 = 5;argp_1 = 30;raan_1 = 10;
[x_1, y_1, z_1, vx_1, vy_1, vz_1] = kep2cart(a_1, e_1, inc_1, raan_1, ... argp_1, v_1);
Y_1 = [x_1, y_1, z_1, vx_1, vy_1, vz_1];
% time_span for two revolutions (depends on the orbit)t1 = [0 (180*60)];
% Setting tolerancesoptions = odeset('RelTol',1e-12,'AbsTol',1e-12);
% Using ODE45 to numerically integrate for LEO[t_1, state_1] = ode45(@OrbitProp, t1, Y_1, options);
function dYdt = OrbitProp(t, Y)
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% State Vector
x = Y(1); % [km]
y = Y(2); % [km]
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Chapter 9 Solutions
Thinking Like an Engineer: An Active Learning Approach (4th Edition)
Ch. 9.1 - The heat loss (Q/t, in units of joules per second...Ch. 9.2 - A simple expression for the velocity of molecules...Ch. 9.2 - What are the dimensions of the value 6 in the...Ch. 9.4 - The Euler number is a function of the pressure...Ch. 9 - Complete the following table. Dimensions ...Ch. 9 - Complete the following table. Dimensions ...Ch. 9 - Calculate the numerical value of each of the...Ch. 9 - Calculate the numerical value of each of the...Ch. 9 - A fluid with a specific gravity of 0.91 and a...Ch. 9 - Brine, with a density of 1.25 grams per cubic...
Ch. 9 - When a simple turbine is used for mixing, the...Ch. 9 - History suggests that Newton developed his idea...Ch. 9 - It is proposed to create a set of dimensionless...Ch. 9 - 1. While researching fluid dynamics, you come...Ch. 9 - 2. While researching fluid dynamics, you came...Ch. 9 - 3. While researching fluid dynamics, you come...Ch. 9 - 4. The Arrhenius number (Ar) is the dimensionless...Ch. 9 - 5. The Biot number (Bi) is the dimensionless...Ch. 9 - 6. A biodegradable fuel having a specific gravity...Ch. 9 - 7. A sludge mixture having a specific gravity of...Ch. 9 - 8. Water (specific gravity = 1.02; viscosity =...Ch. 9 - 9. We have been asked to determine a set of...Ch. 9 - 10. The Peclet number is used in heat transfer in...Ch. 9 - 11. When a fluid flows slowly across a flat plate...Ch. 9 - 12. In modeling the flow of liquid in a piping...
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