A physical quantity hf is determined from the equation hf = (fLv^2) / 2Dg. We are...
A physical quantity hf is determined from the equation hf = (fLv^2) / 2Dg. We are given that f is a dimensionless constant, L is the length, v is the velocity, D is the diameter, and g is the gravitational constant. Analyze hf in terms of fundamental dimensions (mass, length, etc).
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A physical quantity hf is determined from the equation hf =
(fLv^2) / 2Dg. We are...
The hydraulic head loss in a pipe may be determined by the Darcy-Weisbach Equation as follows: H=(f*L*V^2)/(2*D*g) Where...
The hydraulic head loss in a pipe may be determined by the Darcy-Weisbach Equation as follows: H=(f*L*V^2)/(2*D*g) Where L is the length of the pipe, V is the follow velocity of water in a pipe, D is the pipe diameter, f is the coefficient of friction and g is the gravitational acceleration (32.2 ft/sec^2) Suppose the length of the pipe L has a constant length of 10 ft and the pipe has a constant diameter of .5 ft. The coefficient...
Example 1 A star undergoes some mode of oscillation. Scientists/engineers have hypothesized that the oscillation frequency...
Example 1 A star undergoes some mode of oscillation. Scientists/engineers have hypothesized that the oscillation frequency (cycles per second), o, is dependent on the density p and the radius R and the gravitational constant G which appears in Newton's law of universal gravitation. If you are not familiar with the gravitational constant, read the section on mass and weight in Chapter 4 (Dimensions/units) of the text. Therefore, w has dimensions (T), and P, R, Gare the governing parameters, with dimensions...
To examine the speed that a wave can propagate, we will use a simple model of...
To examine the speed that a wave can propagate, we will use a simple model of dominos toppling. A schematic of the system is shown below. Assume the velocity v depends on the spacing d, height h, and the gravitational acceleration constant g. Based on the data provided below, determine the two dimensionless Pi's that govern the wave speed: II1 = G(112) Total number of parameters: n = 4;(v,d, h,g) Number of primary dimensions: r = 2; (Lt) Dimensional parameters:...
01 ) During a study of a certain flow system the following equation was developed: P2=C+4.6'f...
01 ) During a study of a certain flow system the following equation was developed: P2=C+4.6'f LV P. P.Dg where pi an p2 are pressure between points 1 and 2, C is dimensionless constant, V is velocity, L is the distance between the points, D is the diameter, g is acceleration of gravity and f is drag coefficient. Determine the primary dimensions of the coefficient f so that this equation is homogenous. b) A 25-mm-diameter shaft is pulled through a...
4b. Later on, we will study a quantity called hydraulic head (h) which refers to the...
4b. Later on, we will study a quantity called hydraulic head (h) which refers to the mechanical energy in a given mass of fluid. As water flows through a pipe, some amount of this energy, or head, is lost due to friction, and the resulting head loss (4h) can be calculated using the expression Ah = 25 (5) Where L is the length and D the diameter of the pipe, respectively, Vis velocity, g is gravity, and f refers to...
4. Based on the following equation, express the variable q, in terms of fundamental dimensions (mass,...
4. Based on the following equation, express the variable q, in terms of fundamental dimensions (mass, temperature, length, etc.). L = λP² + q where L [=] candela per square inch [cd/in²]; P [=] watt [W]
1. The force F on a propeller of diameter d is given by F = k...
1. The force F on a propeller of diameter d is given by F = k dºvp?, where v is the velocity of the propeller, p is the density of the fluid, k is the dimensionless constant of proportionality, and a, b, and are constant. (a) Find the dimensions of F, d, v and p. (4 marks) (b) Use dimensional analysis to determine the constants a, B, and 7. [6 marks]
d. Show the algebraic steps in deriving equation (5) using equations (1) and (3). Please explain...
d. Show the algebraic steps in deriving equation (5) using
equations (1) and (3).
Please explain this very well.
When a string is stretched between two fixed points, the speed of the waves formed on it is given by the following equation. F (1) V= u Mass of the string per unit length or linear density of the string is given by U= m L (2) Using the general velocity, wavelength and frequency relationship for a wave and considering the...
Given v = (2πr)/T and G = (v^2• r )/ ms Substitute the first equation for...
Given v = (2πr)/T and G = (v^2• r )/ ms Substitute the first equation for velocity into the second and solve for the equation for slope. v = velocity T = period r = radius G= Gravitational Constant ms= mass sun
1. Express the answer to the following problems using the correct number of significant figures a....
1. Express the answer to the following problems using the correct number of significant figures a. 1.144 x 10 20.0 b. 4.77 x 101 -9.16 x 10 2. Express the Boltzmann constant (1.38065 x 102" kg m's K') in units of miles' lb yrK 3. Convert 9.997 x 101 g cm* into kg km 4. The Reynolds number is used to deseribe the conditions of particle settling If the Reynolds number is given by the following equation Where v, is...
Example 1 A star undergoes some mode of oscillation. Scientists/engineers have hypothesized that the oscillation frequency (cycles per second), o, is dependent on the density p and the radius R and the gravitational constant G which appears in Newton's law of universal gravitation. If you are not familiar with the gravitational constant, read the section on mass and weight in Chapter 4 (Dimensions/units) of the text. Therefore, w has dimensions (T), and P, R, Gare the governing parameters, with dimensions...
To examine the speed that a wave can propagate, we will use a simple model of dominos toppling. A schematic of the system is shown below. Assume the velocity v depends on the spacing d, height h, and the gravitational acceleration constant g. Based on the data provided below, determine the two dimensionless Pi's that govern the wave speed: II1 = G(112) Total number of parameters: n = 4;(v,d, h,g) Number of primary dimensions: r = 2; (Lt) Dimensional parameters:...
01 ) During a study of a certain flow system the following equation was developed: P2=C+4.6'f LV P. P.Dg where pi an p2 are pressure between points 1 and 2, C is dimensionless constant, V is velocity, L is the distance between the points, D is the diameter, g is acceleration of gravity and f is drag coefficient. Determine the primary dimensions of the coefficient f so that this equation is homogenous. b) A 25-mm-diameter shaft is pulled through a...
4b. Later on, we will study a quantity called hydraulic head (h) which refers to the mechanical energy in a given mass of fluid. As water flows through a pipe, some amount of this energy, or head, is lost due to friction, and the resulting head loss (4h) can be calculated using the expression Ah = 25 (5) Where L is the length and D the diameter of the pipe, respectively, Vis velocity, g is gravity, and f refers to...
1. The force F on a propeller of diameter d is given by F = k dºvp?, where v is the velocity of the propeller, p is the density of the fluid, k is the dimensionless constant of proportionality, and a, b, and are constant. (a) Find the dimensions of F, d, v and p. (4 marks) (b) Use dimensional analysis to determine the constants a, B, and 7. [6 marks]
d. Show the algebraic steps in deriving equation (5) using
equations (1) and (3).
Please explain this very well.
When a string is stretched between two fixed points, the speed of the waves formed on it is given by the following equation. F (1) V= u Mass of the string per unit length or linear density of the string is given by U= m L (2) Using the general velocity, wavelength and frequency relationship for a wave and considering the...
1. Express the answer to the following problems using the correct number of significant figures a. 1.144 x 10 20.0 b. 4.77 x 101 -9.16 x 10 2. Express the Boltzmann constant (1.38065 x 102" kg m's K') in units of miles' lb yrK 3. Convert 9.997 x 101 g cm* into kg km 4. The Reynolds number is used to deseribe the conditions of particle settling If the Reynolds number is given by the following equation Where v, is...
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