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3. Consider the following description of a mathematical model: a spherical raindrop evap- orates...
2.) As a raindrop falls through a cloud, it collides with smaller droplets of mist and...
2.) As a raindrop falls through a cloud, it collides with smaller droplets of mist and grows in mass (a) Derive a differential equation that relates the mass and velocity of the drop as it falls and accretes mass. Hint: Do NOT just differentiate d(mv)/dt, but start with the impulse-momentum theorem in differential form, like we did in the derivation of the rocket equation. Your "system" should include the raindrop itself and a small mass Δm of droplets with which...
3. (a) Assume that a light ray incident from air on a spherical raindrop of radius R at angle measured with respect...
3. (a) Assume that a light ray incident from air on a spherical raindrop of radius R at angle measured with respect to the surface normal undergoes one internal reflection before leaving the raindrop, as shown below. refraction Incident ray Internal reflection A refraction Use the area above to show that if ; = 0 and 2 = @it, then the total deflection angle 8 = 8 + 8 + 83 of the light ray is (in radians): 8 =...
3. (a) Assume that a light ray incident from air on a spherical raindrop of radius R at angle 0 measured with respe...
3. (a) Assume that a light ray incident from air on a spherical raindrop of radius R at angle 0 measured with respect to the surface normal undergoes one internal reflection before leaving the raindrop, as shown below. refraction Internal Incident reflection 8 ray R refraction Use the area above to show that if e0 and e 0t, then the total deflection angle & 8+88 of the light ray is (in radians): 8 2(0,-0)+- 20, The deflection angle & is...
Write the vector differential operator "DEL-V in Cartesian coordinates Cylindrical coordinates Spherical coordinates. 2. Show for...
Write the vector differential operator "DEL-V in Cartesian coordinates Cylindrical coordinates Spherical coordinates. 2. Show for any "nice" scalar function (x,y,z), the Curl of the gradient of (x,y,z) is Zero.. VxVo = 0 Hint: assume the order of differentiation can be switched 3. Find the volume of a sphere of radius R by integrating the infinitesimal volume element of the sphere. 4. Write Maxwell's equations for the case of electro and magneto statics (the fields do not change in time)...
Question 18: A fungus is spreading on the surface of a wall. A biologist proposes a...
Question 18: A fungus is spreading on the surface of a wall. A biologist proposes a model for the rate at which the fungus is spreading on the wall. The total surface area of the wall is 9 m². The surface area that is affected at time t hours is x m². The biologist proposes that the rate of change of x is proportional to the product of the surface area that is affected and the surface area that is...
3. Consider a tank which initially contains V litres of water and Qo kilograms of salt....
3. Consider a tank which initially contains V litres of water and Qo kilograms of salt. Suppose that a new mixture of brine at a concentration of k kg per litre is poured into the tank, the contents of the vat are thoroughly mixed, and the contents of the tank are drained at the same rate. Unlike the model we studied in class, however, now assume that the rate of inflow and outflow is proportional to the length of time...
O/ Write an appropriate mathematical model for this problem including Decision Variables and their description, Objective...
O/ Write an appropriate mathematical model for this problem including Decision Variables and their description, Objective Function, & Constraints. XAMPLE 4.3 AGGREGATE PLANNING AT SURESTEP uring the next four months the SureStep Company must meet (on time) the fol lowing demands for pairs of shoes: 3000 in month 1 5000 in month 2; 2000 in month 3; and 1000 in month 4. At the beginning of month 1, 500 pairs of shoes are on hand, and SureStep has 100 workers....
Consider the following conical drainage collector of side angle α: You can assume that the liquid level is perfectly flat. All of the liquid in the tank is considered incompressible, and must satisfy...
Consider the following conical drainage collector of side angle α: You can assume that the liquid level is perfectly flat. All of the liquid in the tank is considered incompressible, and must satisfy Bernoulli's equation: PV2pgh -constant 2 You can assume that the height at the bottom is the baseline (h2 -0). the liquid line velocity is minimal (Vi 0). and that the pressure is equalized (Pi P2). The height of the liquid line being tracked is equal to the...
please, solve by explaning :) Consider an Am-Be neutron source placed inside a spherical water tank...
please, solve by explaning :)
Consider an Am-Be neutron source placed inside a spherical water tank with a radius of R The source (assuming point source) emits S neutrons per second. For this experimental setup, students should (a) State energy of the neutrons released from the source. (b) Write time-dependent two-group neutron diffusion equation for the source. (c) Give boundary conditions necessary to solve the equations you obtained in (b). (d) Draw fast and thermal fluxes as a function of...
Consider the following mathematical model used to predict the mass of a single largemouth fish (bass)...
Consider the following mathematical model used to predict the mass of a single largemouth fish (bass) caught from a fish population present in a lake: Fish Mass (lbm) = 11 – [Random(1,100)]½ Where the function Random (1,100) returns any integer between 1 and 100 with equal probability for a particular fish caught. Based on this model, what can you say about: a. The range of fish mass predicted by the model? b. Does the model predict a Normal (aka Gaussian,...
2.) As a raindrop falls through a cloud, it collides with smaller droplets of mist and grows in mass (a) Derive a differential equation that relates the mass and velocity of the drop as it falls and accretes mass. Hint: Do NOT just differentiate d(mv)/dt, but start with the impulse-momentum theorem in differential form, like we did in the derivation of the rocket equation. Your "system" should include the raindrop itself and a small mass Δm of droplets with which...
3. (a) Assume that a light ray incident from air on a spherical raindrop of radius R at angle measured with respect to the surface normal undergoes one internal reflection before leaving the raindrop, as shown below. refraction Incident ray Internal reflection A refraction Use the area above to show that if ; = 0 and 2 = @it, then the total deflection angle 8 = 8 + 8 + 83 of the light ray is (in radians): 8 =...
3. (a) Assume that a light ray incident from air on a spherical raindrop of radius R at angle 0 measured with respect to the surface normal undergoes one internal reflection before leaving the raindrop, as shown below. refraction Internal Incident reflection 8 ray R refraction Use the area above to show that if e0 and e 0t, then the total deflection angle & 8+88 of the light ray is (in radians): 8 2(0,-0)+- 20, The deflection angle & is...
Write the vector differential operator "DEL-V in Cartesian coordinates Cylindrical coordinates Spherical coordinates. 2. Show for any "nice" scalar function (x,y,z), the Curl of the gradient of (x,y,z) is Zero.. VxVo = 0 Hint: assume the order of differentiation can be switched 3. Find the volume of a sphere of radius R by integrating the infinitesimal volume element of the sphere. 4. Write Maxwell's equations for the case of electro and magneto statics (the fields do not change in time)...
Question 18: A fungus is spreading on the surface of a wall. A biologist proposes a model for the rate at which the fungus is spreading on the wall. The total surface area of the wall is 9 m². The surface area that is affected at time t hours is x m². The biologist proposes that the rate of change of x is proportional to the product of the surface area that is affected and the surface area that is...
3. Consider a tank which initially contains V litres of water and Qo kilograms of salt. Suppose that a new mixture of brine at a concentration of k kg per litre is poured into the tank, the contents of the vat are thoroughly mixed, and the contents of the tank are drained at the same rate. Unlike the model we studied in class, however, now assume that the rate of inflow and outflow is proportional to the length of time...
O/ Write an appropriate mathematical model for this problem including Decision Variables and their description, Objective Function, & Constraints. XAMPLE 4.3 AGGREGATE PLANNING AT SURESTEP uring the next four months the SureStep Company must meet (on time) the fol lowing demands for pairs of shoes: 3000 in month 1 5000 in month 2; 2000 in month 3; and 1000 in month 4. At the beginning of month 1, 500 pairs of shoes are on hand, and SureStep has 100 workers....
Consider the following conical drainage collector of side angle α: You can assume that the liquid level is perfectly flat. All of the liquid in the tank is considered incompressible, and must satisfy Bernoulli's equation: PV2pgh -constant 2 You can assume that the height at the bottom is the baseline (h2 -0). the liquid line velocity is minimal (Vi 0). and that the pressure is equalized (Pi P2). The height of the liquid line being tracked is equal to the...
please, solve by explaning :)
Consider an Am-Be neutron source placed inside a spherical water tank with a radius of R The source (assuming point source) emits S neutrons per second. For this experimental setup, students should (a) State energy of the neutrons released from the source. (b) Write time-dependent two-group neutron diffusion equation for the source. (c) Give boundary conditions necessary to solve the equations you obtained in (b). (d) Draw fast and thermal fluxes as a function of...
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