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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Textbook Question
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)
mu = 3.986*10^5; % Earth's gravitational parameter [km^3/s^2]
% State Vector
x = Y(1); % [km]
y = Y(2); % [km]
z = Y(3); % [km]
vx = Y(4);…
Pressure drop AP depends on four variables: the diameter of the pipe D, the density of the fluid p, the
kinematic viscosity of the fluid v and the mean velocity v. Applying Buckinham's Pi Theorem, a
dimensionless pi-group can be identified using the following power product: [AP] = [D]ª[p]b[v][v]ª.
Which of the following statements in term of [T] is correct?
Select one:
O
[T]: -2 = -c-d
[T]: -1 = -c-d
[T]: -2 = -c-2*d
[T]: -2 = -2*c-d
[T]: -2=-c+d
3. Consider the following equation. All three of the terms in parentheses are dimensionless groups.
Because kc is difficult to determine directly, the other variables are measured and kc is calculated
from the given equation.
26
THERMODYNAMICS 1
MODULE 1
FUNDAMENTAL CONCEPTS
]3 [ _d>vp_jo8
p DAB
kc D
= 0.023 [H
DAB
What is the estimated value of kc? What are the units of kc? Show your work.
The following values were measured:
D = 8.0 mm, DAB = 0.475 cm²/s, µ = 1.12 x 103 N-s/m², p = 1.00 x 10-³ g/cm³, v = 15.0 m/s.
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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