Euler's equation and ideal fluid question:
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Euler's equation and ideal fluid question:
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Advanced Fluid Mechanics For an inviscid fluid we have Euler's equation (vectors are denoted by bold characters)...
Advanced Fluid Mechanics
For an inviscid fluid we have Euler's equation (vectors are denoted by bold characters) )= Vp - Vgx + V xu at and whether or not the fluid is incompressible, we also have the conservation of mass Dp +pv u 0. Dt Show that x Vp Dt Deduce that, if p is a function of palone, the vorticity equation is exactly as in the incompressible, constant density case, except that ois replaced by ap.
For an inviscid...
In addition, derive the "wave equation" for an incompressible fluid. Use the continuity equation and the...
In addition, derive the "wave equation" for an incompressible
fluid. Use the continuity equation and the linearized euler
equation.
Linearized Euler:
A flow is incompressible if a fluid element does not change its density as the element moves. From Problem 54.1, this means (7p/dt) u . ρ-0. (a) Show that for an incompressible fluid the equation of continuity reduces to V -u -0. (b) Write Euler's equation for the flow of an incompressible fluid. (c) What is c for an...
1. Consider the following differential equation. ag = ty, y(0)=1. dt (a) Use Euler's Method with...
1. Consider the following differential equation. ag = ty, y(0)=1. dt (a) Use Euler's Method with At = .1 to approximate y(1). (b) Use Euler's Method with At = .05 to approximate y(1). (c) Find the exact solution to the problem. Use this solution to compare the error for the different values of At. What does this say about the method? Note: On the course page there are notes describing an implementation of Euler's method on a spread sheet.
Question 9 2 pts dt -ay, where Using Euler's method on a system of the form...
Question 9 2 pts dt -ay, where Using Euler's method on a system of the form dy a is a positive constant, results in the equation Yi+1 yi (1 - ah). What is the condition for the solution to be stable? 0 |1 - ah| > 1 0 |1 - ah| > 0 o 1 - ah] < 0 o 1 - ahl <1 Question 10 2 pts Partial differential equations have a single independent variable. O True False
can you post the answer in matlab and code Question 1: Euler's Method. A simple circuit...
can
you post the answer in matlab and code
Question 1: Euler's Method. A simple circuit having resistance R, in- ductance L, and capacitance C in parallel has a current i(t) that satisfies the differential equation 1 dV + R dt V di C dt2 www. dt Take parameters C 0.3 farads, R assume that the applied voltage to the circuit is given by 1.4 olms, andL= 1.7 henries and -0.06t sin(2t). V (t) e Using Euler's method, approximate the...
Show that the relativistic equation ot motion can be written in the form (V.f) Mo dv...
Show that the relativistic equation ot motion can be written in the form (V.f) Mo dv 1-(v/c)]' Y2 dt point charge, and that i t is the Lorent2 torce on a qlE+ VxB), the right-hand side becomes 9E+VxB- Iv. E) /c 1 v
Show that the relativistic equation ot motion can be written in the form (V.f) Mo dv 1-(v/c)]' Y2 dt point charge, and that i t is the Lorent2 torce on a qlE+ VxB), the right-hand side becomes...
i have a question about euler's formula when euler's formula suggets that e^j(angle) is e^j(angle) =...
i have a question about euler's formula when euler's formula suggets that e^j(angle) is e^j(angle) = cos (angle) + jsin(angle) is e^-j2pi equal to 1? or negative 1? because my professor treated e^-j2pi as 1 would e^-j2pi be equal to cos(-2pi) + jsin(-2pi) or -cos(2pi) - jsin(2pi) or -(cos(-2pi) + jsin(-2pi)) first one would be 1 and second and third one would be negative one right? i think its second one i dont know why professor assumed e^-j2pi as 1...
Find the time constant t of the following differential equation: a(dy/dt)+by+cx=e(dx/dt)+f(dy/dt)...
Find the time constant t of the following differential
equation: a(dy/dt)+by+cx=e(dx/dt)+f(dy/dt)+g, of the given that x
is the inout, y is the output, and a through g are constants.
13, Find the time constant τ from the following differential equation, dt dt given that x is the input, y is the output and, a through g are constants. It is known that for a first-order instrument with differential equation a time constant r- alao dy the
13, Find the time...
MATLAB CODE: Task 2 8y dt Solve the above ordinary differential equation (ODE) using Euler's method with step sizes of: 2. h 0.75 3. h 0.5 4. h 0.001 a) For each step size, plot the results at eac...
MATLAB CODE:
Task 2 8y dt Solve the above ordinary differential equation (ODE) using Euler's method with step sizes of: 2. h 0.75 3. h 0.5 4. h 0.001 a) For each step size, plot the results at each step starting from y(0) 3 to y(3). b) Plot on the same figure as part a) the analytical solution which is given by: 9 24 -8t c) Calculate and print the percentage error between the Euler's method and the analytical result...
#2: Consider the ideal lowpass filter DT filter described by -j60 e 4 0, 4 H()...
#2: Consider the ideal lowpass filter DT filter described by -j60 e 4 0, 4 H() | 2,7 - periodic elsewhere (a) (10 pts) Find the output for an input signal x[n]=2 cosnr/2 (b) (10 pts) Find the output for an input signal xnsinc (n /2) (c) (10 pts) Find the output for an input signal x[n]sinc(n/8) cos (n)
#2: Consider the ideal lowpass filter DT filter described by -j60 e 4 0, 4 H() | 2,7 - periodic elsewhere...
Advanced Fluid Mechanics
For an inviscid fluid we have Euler's equation (vectors are denoted by bold characters) )= Vp - Vgx + V xu at and whether or not the fluid is incompressible, we also have the conservation of mass Dp +pv u 0. Dt Show that x Vp Dt Deduce that, if p is a function of palone, the vorticity equation is exactly as in the incompressible, constant density case, except that ois replaced by ap.
For an inviscid...
In addition, derive the "wave equation" for an incompressible
fluid. Use the continuity equation and the linearized euler
equation.
Linearized Euler:
A flow is incompressible if a fluid element does not change its density as the element moves. From Problem 54.1, this means (7p/dt) u . ρ-0. (a) Show that for an incompressible fluid the equation of continuity reduces to V -u -0. (b) Write Euler's equation for the flow of an incompressible fluid. (c) What is c for an...
1. Consider the following differential equation. ag = ty, y(0)=1. dt (a) Use Euler's Method with At = .1 to approximate y(1). (b) Use Euler's Method with At = .05 to approximate y(1). (c) Find the exact solution to the problem. Use this solution to compare the error for the different values of At. What does this say about the method? Note: On the course page there are notes describing an implementation of Euler's method on a spread sheet.
Question 9 2 pts dt -ay, where Using Euler's method on a system of the form dy a is a positive constant, results in the equation Yi+1 yi (1 - ah). What is the condition for the solution to be stable? 0 |1 - ah| > 1 0 |1 - ah| > 0 o 1 - ah] < 0 o 1 - ahl <1 Question 10 2 pts Partial differential equations have a single independent variable. O True False
can
you post the answer in matlab and code
Question 1: Euler's Method. A simple circuit having resistance R, in- ductance L, and capacitance C in parallel has a current i(t) that satisfies the differential equation 1 dV + R dt V di C dt2 www. dt Take parameters C 0.3 farads, R assume that the applied voltage to the circuit is given by 1.4 olms, andL= 1.7 henries and -0.06t sin(2t). V (t) e Using Euler's method, approximate the...
Show that the relativistic equation ot motion can be written in the form (V.f) Mo dv 1-(v/c)]' Y2 dt point charge, and that i t is the Lorent2 torce on a qlE+ VxB), the right-hand side becomes 9E+VxB- Iv. E) /c 1 v
Show that the relativistic equation ot motion can be written in the form (V.f) Mo dv 1-(v/c)]' Y2 dt point charge, and that i t is the Lorent2 torce on a qlE+ VxB), the right-hand side becomes...
Find the time constant t of the following differential
equation: a(dy/dt)+by+cx=e(dx/dt)+f(dy/dt)+g, of the given that x
is the inout, y is the output, and a through g are constants.
13, Find the time constant τ from the following differential equation, dt dt given that x is the input, y is the output and, a through g are constants. It is known that for a first-order instrument with differential equation a time constant r- alao dy the
13, Find the time...
MATLAB CODE:
Task 2 8y dt Solve the above ordinary differential equation (ODE) using Euler's method with step sizes of: 2. h 0.75 3. h 0.5 4. h 0.001 a) For each step size, plot the results at each step starting from y(0) 3 to y(3). b) Plot on the same figure as part a) the analytical solution which is given by: 9 24 -8t c) Calculate and print the percentage error between the Euler's method and the analytical result...
#2: Consider the ideal lowpass filter DT filter described by -j60 e 4 0, 4 H() | 2,7 - periodic elsewhere (a) (10 pts) Find the output for an input signal x[n]=2 cosnr/2 (b) (10 pts) Find the output for an input signal xnsinc (n /2) (c) (10 pts) Find the output for an input signal x[n]sinc(n/8) cos (n)
#2: Consider the ideal lowpass filter DT filter described by -j60 e 4 0, 4 H() | 2,7 - periodic elsewhere...
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