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di- ßude use equation du = Bu dT - RodP and ds=ce ce di to develop...
Determine the Reynolds-averaged x-momentum equation in Cartesian coordinates starting from the equation provided. Du Dt ax o Du Dt ax o
Determine the Reynolds-averaged x-momentum equation in Cartesian
coordinates starting from the equation provided.
Du Dt ax o
Du Dt ax o
(1 point) Use the chain rule to find du dt where w = x+y4 + y...
(1 point) Use the chain rule to find du dt where w = x+y4 + y 25, x = e', y = e' sint, z = = e cost First the pieces oho д ㅋㅋ Thu d Now all together Bu da dt er de Che dy y de is too horrible to write down (correctly). 3: di
Consider the second version of the Lotka-Volterra model: dF F(a - 6F - cS) dt ds...
Consider the second version of the Lotka-Volterra model: dF F(a - 6F - cS) dt ds = S(-k + XF). dt (1) Explain the model; i.e. what are the terms in the equation signify? How is this model different from equations (1)? (2) Find the equilibrium point(s). (3) Linearize (2) about the equilibrium point(s). (4) Classify if the equilibrium points are stable or unstable. (5) Pick some values for a, b,c,k, X. Plot the solutions of the model and the...
Differential Equation 3.2.015
A differential equation for the velocity v of a falling mass m subjected to air resistance proportional to the square of the instantaneous velocity ism(dv/dt) = mg − kv2,k > 0 is a constant of proportionality. The positive direction is downward.(a) Solve the equation subject to the initial condition v(0) = v0.(b) Use the solution in part (a) to determine the limiting, or terminal, velocity of the mass.(c) If the distance s, measured from the point where the mass was released above ground, is related to velocity v by ds/dt = v(t), find an explicit expression for s(t) if...
the S-I-R model 3. In a school of 150 students, one of the students has the flu initially (a) What is Io? What is So? (b) Use these values of Io and So and the equation dI dS 0.0002651-0.51 to d...
the
S-I-R model
3. In a school of 150 students, one of the students has the flu initially (a) What is Io? What is So? (b) Use these values of Io and So and the equation dI dS 0.0002651-0.51 to determine whether the number of infected people ini- tially increase or decreases. (c) What does this tell you about the spread of the disease? (d) Calculate the formulas for S(t) and I(t)
3. In a school of 150 students, one...
1.) The rocket equation in 1 dimension is ert dt dt where u is the exhaust...
1.) The rocket equation in 1 dimension is ert dt dt where u is the exhaust velocity (in the rocket frame) and Fe is the net external force on the rocket Consider a space probe that is traveling through an interstellar cloud (far from any large gravitational masses). The probe experiences a linear drag force FD - -bv. Let us also assume that u is constant and dm/dt =-γ is constant. (a) The probe runs out of fuel when the...
Heat is transferred to a gas in a piston cylinder device so that the volume changes...
Heat is transferred to a gas in a piston cylinder device so that the volume changes from 3 mºto 6 m2. The initial pressure and temperature of the gas are 400 kPa and 25°C. If the process is irreversible determine the following: 1- The final temperature of the gas. 2- The work done during the process (kJ). 3- The total change in internal energy (kJ). 4- The heat transfer for the process (kJ). 5- The total entropy change (kJ/K). Comment...
In (14) of Section 1.3 we saw that a differential equation describing the velocity v of...
In (14) of Section 1.3 we saw that a differential equation describing the velocity v of a falling mass subject to air resistance proportional to the instantaneous velocity is dv dt where k> 0 is a constant of proportionality. The positive direction is downward (a) Solve the equation subject to the initial condition vo)o (b) Use the solution in part (a) to determine the limiting, or terminal, velocity of the mass c) If the distance s measured from the point...
Consider a point charge q moving arbitrar ily along a trajectory described by vector function of time r (t). The velocity of the charge is thus V(t)- di,(t)/dt. Suppose Q and Q'represent points o...
Consider a point charge q moving arbitrar ily along a trajectory described by vector function of time r (t). The velocity of the charge is thus V(t)- di,(t)/dt. Suppose Q and Q'represent points on the trajectory where the charge is at time t and was at an earlier time t'. Let R(t) F r,(t) be the vector from the charge to the fixed point P as shown in the figure of particle re volume element de r" a) Prove the...
1. Civil engineers use the continuity equation for many applications. This simple ordinary differential equation states...
1. Civil engineers use the continuity equation for many applications. This simple ordinary differential equation states that the difference between (volumetric) rates of inflow and outflow is equal to the rate of change of storage in the system: I- o- dS/dt where S is storage or volume and t is time Consider a conical tank with top radius, r-1.83 meters and height, h- 3.05 meters. Thetank is initially empty, and then water is added at a rate of I- 0.00095...
Determine the Reynolds-averaged x-momentum equation in Cartesian
coordinates starting from the equation provided.
Du Dt ax o
Du Dt ax o
(1 point) Use the chain rule to find du dt where w = x+y4 + y 25, x = e', y = e' sint, z = = e cost First the pieces oho д ㅋㅋ Thu d Now all together Bu da dt er de Che dy y de is too horrible to write down (correctly). 3: di
Consider the second version of the Lotka-Volterra model: dF F(a - 6F - cS) dt ds = S(-k + XF). dt (1) Explain the model; i.e. what are the terms in the equation signify? How is this model different from equations (1)? (2) Find the equilibrium point(s). (3) Linearize (2) about the equilibrium point(s). (4) Classify if the equilibrium points are stable or unstable. (5) Pick some values for a, b,c,k, X. Plot the solutions of the model and the...
the
S-I-R model
3. In a school of 150 students, one of the students has the flu initially (a) What is Io? What is So? (b) Use these values of Io and So and the equation dI dS 0.0002651-0.51 to determine whether the number of infected people ini- tially increase or decreases. (c) What does this tell you about the spread of the disease? (d) Calculate the formulas for S(t) and I(t)
3. In a school of 150 students, one...
1.) The rocket equation in 1 dimension is ert dt dt where u is the exhaust velocity (in the rocket frame) and Fe is the net external force on the rocket Consider a space probe that is traveling through an interstellar cloud (far from any large gravitational masses). The probe experiences a linear drag force FD - -bv. Let us also assume that u is constant and dm/dt =-γ is constant. (a) The probe runs out of fuel when the...
Heat is transferred to a gas in a piston cylinder device so that the volume changes from 3 mºto 6 m2. The initial pressure and temperature of the gas are 400 kPa and 25°C. If the process is irreversible determine the following: 1- The final temperature of the gas. 2- The work done during the process (kJ). 3- The total change in internal energy (kJ). 4- The heat transfer for the process (kJ). 5- The total entropy change (kJ/K). Comment...
In (14) of Section 1.3 we saw that a differential equation describing the velocity v of a falling mass subject to air resistance proportional to the instantaneous velocity is dv dt where k> 0 is a constant of proportionality. The positive direction is downward (a) Solve the equation subject to the initial condition vo)o (b) Use the solution in part (a) to determine the limiting, or terminal, velocity of the mass c) If the distance s measured from the point...
Consider a point charge q moving arbitrar ily along a trajectory described by vector function of time r (t). The velocity of the charge is thus V(t)- di,(t)/dt. Suppose Q and Q'represent points on the trajectory where the charge is at time t and was at an earlier time t'. Let R(t) F r,(t) be the vector from the charge to the fixed point P as shown in the figure of particle re volume element de r" a) Prove the...
1. Civil engineers use the continuity equation for many applications. This simple ordinary differential equation states that the difference between (volumetric) rates of inflow and outflow is equal to the rate of change of storage in the system: I- o- dS/dt where S is storage or volume and t is time Consider a conical tank with top radius, r-1.83 meters and height, h- 3.05 meters. Thetank is initially empty, and then water is added at a rate of I- 0.00095...
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