Homework Answers
Note: Using the excel sheet,
one can find the friction factor f easily. In the first case, I
have solved manually by the fact that the left-hand side (LHS) of
the Colebrook equation is equal to the right-hand side (RHS). If
the sign of the value changes from negative to positive the value
of friction factor lies in between that so again iterate between
that value (see above excel sheet).
In the second case, I have used solver to solve for friction factor f. In Excel go to date--> pick the solver --> select the set target cell (your difference column) --> Equal To: Value of 0 --> By Changing Cells (your Guess value of f) --> Options --> Convergence (0.000001) --> tick to Use Automatic Scaling --> Estimates (Quadratic) --> Ok --> solve --> Now you will get the value of friction factor f
Hence the friction factor f value here is 0.02061679
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Indirect method In CAD
Example 1.7: The Colebrook equation is given by ED 2.51 Find the...
2. The Colebrook equation for the Darcy friction factor, f, is written as: ./1/f + 0.86 In(y +2.51 3.7 NRevf For a...
2. The Colebrook equation for the Darcy friction factor, f, is written as: ./1/f + 0.86 In(y +2.51 3.7 NRevf For a Reynolds number (NRe) of 10% and a roughness factor, E/D, of 10, a) Show that there exists a root in the interval 0.001 0.1]. (1 mark) b) Find the number of iterations of the bisection method required to get a true absolute error of 10. (3 marks) c) Show two full iterations of the bisection method for this...
scouS in a pipe are expre in terms of a Jriction Jactor, J. It is important to frictional forces in pipe flow because t...
scouS in a pipe are expre in terms of a Jriction Jactor, J. It is important to frictional forces in pipe flow because they result in pressure loss which must be accounted for in the piping system. For turbulent flow in pipes, the friction factor is calculated using the Colebrook equation: e/D 2.51 VT where e is the roughness height, D is the pipe diameter and Re is the pipe Reynolds number (dimensionless). For e/D = 0.008 and Re =...
please answer b. and c. Problem 1. Consider the differential equation given by (a) On the...
please answer b. and c.
Problem 1. Consider the differential equation given by (a) On the axes provided below, sketch a slope field for the given differential equation at the nine points indicated. locales de mor t e wold qolution to the given differential equation with the initial condition (b) Let y = f(x) be the particular solution to the given differential equation with the initial condition f(0) = 3. Use Euler's method starting at x = 0, with a...
Use the method of undetermined coefficients to find a particular solution to the given higher-order equation....
Use the method of undetermined coefficients to find a particular solution to the given higher-order equation. 9y'"' + 3y'' +y' – 2y = e = A solution is yp(t)=
c++ Newton method for iteratively finding the root f(x) = 0. The equation is Where f(x)...
c++
Newton method for iteratively finding the root f(x) = 0. The equation is Where f(x) is the function, f'(x) is the derivative of f9x), Write a C++ program to find root for the function of f(x). The function is on your C++ homework 2 for F(x) = x + 2x -10 You may have two functions, for example, float f(float x) float f=x*x-4; //any function equation return f; float prime(float x) float prime = 2 * x; //derivative of...
Proceed as in this example to find a particular solution y(x) of the given diferential equation...
Proceed as in this example to find a particular solution y(x) of the given diferential equation in the Integral formy.(x) = f* 3- / Gx, 0) G(x, t) (1) dt. y" + 25y = f(x) Y(X) LO Dres dt
Use the method of reduction of order to find the general solution to x2r"-xy'+y =x given that 3'1 = x is a solution to the complementary equation 1. Use the method of reduction o...
Use the method of reduction of order to find the general solution to x2r"-xy'+y =x given that 3'1 = x is a solution to the complementary equation 1.
Use the method of reduction of order to find the general solution to x2r"-xy'+y =x given that 3'1 = x is a solution to the complementary equation 1.
Use the solution method from this example to find a basis for the given subspace. 1...
Use the solution method from this example to find a basis for the given subspace. 1 4 0 5 1 S = span -1 0 -1 4 0 5 Give the dimension of the basis.
Use the method of variation of parameters to find a particular solution of the given differential...
Use the method of variation of parameters to find a particular solution of the given differential equation. Then check your answer by using the method of indetermined codents V 2'y e ! YTE)
A nonhomogeneous second-order linear equation and a complementary function ye are given below. Use the method...
A nonhomogeneous second-order linear equation and a complementary function ye are given below. Use the method of variation of parameters to find a particular solution of the given differential equation. Before applying the method of variation of parameters, divide the equation by its leading coefficient x2 to rewrite it in the standard form, y" + P(x)y'+Q(x)y = f(x) x2y"xy'y Inx; y c1 cos (In x) + c2 sin (In x) The particular solution is yo (x)
2. The Colebrook equation for the Darcy friction factor, f, is written as: ./1/f + 0.86 In(y +2.51 3.7 NRevf For a Reynolds number (NRe) of 10% and a roughness factor, E/D, of 10, a) Show that there exists a root in the interval 0.001 0.1]. (1 mark) b) Find the number of iterations of the bisection method required to get a true absolute error of 10. (3 marks) c) Show two full iterations of the bisection method for this...
scouS in a pipe are expre in terms of a Jriction Jactor, J. It is important to frictional forces in pipe flow because they result in pressure loss which must be accounted for in the piping system. For turbulent flow in pipes, the friction factor is calculated using the Colebrook equation: e/D 2.51 VT where e is the roughness height, D is the pipe diameter and Re is the pipe Reynolds number (dimensionless). For e/D = 0.008 and Re =...
please answer b. and c.
Problem 1. Consider the differential equation given by (a) On the axes provided below, sketch a slope field for the given differential equation at the nine points indicated. locales de mor t e wold qolution to the given differential equation with the initial condition (b) Let y = f(x) be the particular solution to the given differential equation with the initial condition f(0) = 3. Use Euler's method starting at x = 0, with a...
Use the method of undetermined coefficients to find a particular solution to the given higher-order equation. 9y'"' + 3y'' +y' – 2y = e = A solution is yp(t)=
c++
Newton method for iteratively finding the root f(x) = 0. The equation is Where f(x) is the function, f'(x) is the derivative of f9x), Write a C++ program to find root for the function of f(x). The function is on your C++ homework 2 for F(x) = x + 2x -10 You may have two functions, for example, float f(float x) float f=x*x-4; //any function equation return f; float prime(float x) float prime = 2 * x; //derivative of...
Proceed as in this example to find a particular solution y(x) of the given diferential equation in the Integral formy.(x) = f* 3- / Gx, 0) G(x, t) (1) dt. y" + 25y = f(x) Y(X) LO Dres dt
Use the method of reduction of order to find the general solution to x2r"-xy'+y =x given that 3'1 = x is a solution to the complementary equation 1.
Use the method of reduction of order to find the general solution to x2r"-xy'+y =x given that 3'1 = x is a solution to the complementary equation 1.
Use the solution method from this example to find a basis for the given subspace. 1 4 0 5 1 S = span -1 0 -1 4 0 5 Give the dimension of the basis.
Use the method of variation of parameters to find a particular solution of the given differential equation. Then check your answer by using the method of indetermined codents V 2'y e ! YTE)
A nonhomogeneous second-order linear equation and a complementary function ye are given below. Use the method of variation of parameters to find a particular solution of the given differential equation. Before applying the method of variation of parameters, divide the equation by its leading coefficient x2 to rewrite it in the standard form, y" + P(x)y'+Q(x)y = f(x) x2y"xy'y Inx; y c1 cos (In x) + c2 sin (In x) The particular solution is yo (x)
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