![? When is it applied? Write the equation of a differential mass balance in its most general form showing the notation used. 2 (a) What is a differential mass balance 3 marks] Methanol is added to a storage tank containing 900 kg of methanol at a rate of 1500 kg b1 and is simultaneously withdrawn at a rate that increases linearly with time. The initial rate of withdrawal of methanol is 600 kg h1. Five hours later the rate of withdrawal equals 1000 kg h- Write the general differential mass balance equation applied to the mass of [4 marks] (b) methanol in the tank inserting the values of the parameters given in it. Derive an expression for the methanol withdrawal rate as a function of time. (c) (d) (e) ( [3 marks] Solve the mass balance equation in 2(b) to obtain an expression for the [3 marks methanol mass in the tank as a function of time. Calculate how long it will take for the mass of methanol in the tank to reach its maximum value and calculate that value. 4 marks] Calculate the time it will take to empty the tank [3 marks]](http://img.homeworklib.com/questions/b0294970-5076-11eb-b6fd-6f7ac4e2d277.png?x-oss-process=image/resize,w_560)
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? When is it applied? Write the equation of a differential mass balance in its most...
In a decontamination plant, we have the following tank system: a) Write the differential equation allowing...
In a decontamination plant, we have the following tank system:
a) Write the differential equation allowing to model the quantity of pollutant in the tank A and solve this differential equation.
b) Write the differential equation allowing to model the variation of the volume in the tank B.
c) Write the differential equation allowing to model the quantity of pollutant in the tank B and solve this differential equation.
d) When does the volume of tank B reach 200 liters?...
The position x of a mass m attached to a spring obeys the differential equation i...
The position x of a mass m attached to a spring obeys the differential equation i + yi + w?x = 0 where y 2w. a) (2 marks) Write down expressions for the forces on the mass due to (i) the spring, and (ii) damping. (3 marks) Using a trial solution x = Ae"', show that a = --y/2 ± (y2/4 - «2)1/2 b) c) (4 marks) Show, by finding wd, that the solution is a damped oscillation of the...
Self Test 2 balance) (Unsteady State mass 1 Problem Statement A Vertical tank of diameter D...
Self Test 2 balance) (Unsteady State mass 1 Problem Statement A Vertical tank of diameter D and height H has a narrow crack of width W running vertically from top to bottom. If the tank is initially filled with water and alilowed to drain through the crack under the influence of gravity a) Calculate the output volumetric flow rate at any time t Imagine the crack to be a seties of adiacenr orifices, then, integrate to find the total efflux...
Please answer this problem FULLY with detail steps on how to slove. My professor normally has us ...
Please answer this problem FULLY with detail steps on how to
slove. My professor normally has us answer these questions by hand,
and for complex imformation to put the rest into Excel. So, the
handworked steps and solutions would be greatly apprecited. Thank
you!
For the following problems you must develop a diagram to show the situation, include a brief problem statement and clearly show the energy balance equations you are using (start from the appropriate form of the energy...
Self Test 2 (Unsteady State mass balance) 1. Problem Statement A Vertical tank of diameter D...
Self Test 2 (Unsteady State mass balance) 1. Problem Statement A Vertical tank of diameter D and height H has a narrow crack of width W running vertically from top to bottom. If the tank is initially filled with water and ailowed to drain through the crack under the influence of gravity; a) Calculate the output volumetric flow rate at any time t Imagine the crack to be a series of adjacent orifices, then, integrate to find the total efflux...
(a) The differential equation describing the motion of a stretched string 4. can be writ- ten y T Define the symbol...
(a) The differential equation describing the motion of a stretched string 4. can be writ- ten y T Define the symbols that appear in this equation. [3 marks] (b) A uniform stretched string has length 2 m, mass 40 g and a fundamental fre- quency of 75 Hz. [4 marks] (i) Calculate the tension in the string. (ii) Write explicit expressions for the two lowest frequency normal modes of the string and sketch their shapes. (iii) The string is pulled...
Spring mass damper system with forced response, the forced system given by the equation For damping...
Spring mass damper system with forced response, the forced system given by the equation For damping factor:E-0.1 ; mass; m-| kg: stiffness of spring; k-100 Nm; f-| 00 N; ω Zun; initial condition: x (0)-2 cms; r(0) = 0. fsincot Task Marks 1. Write down the reduced equation into 2first orderns Hand written equations differential equations 2. Rearrange equation (1) with the following generalized equation 250, x+osinor calculations 3. Calculate the value of c calculations Hand calculations 4. Using the...
Elementary Differential Equation Unit Step Function Problem Project 2 A Spring-Mass Event Problenm A mass of...
Elementary Differential Equation Unit Step Function Problem
Project 2 A Spring-Mass Event Problenm A mass of magnitude m is confined to one-dimensional motion between two springs on a frictionless horizontal surface, as shown in Figure 4.P.3. The mass, which is unattached to either spring, undergoes simple inertial motion whenever the distance from the origin of the center point of the mass, x, satisfies lxl < L. When x 2 L, the mass is in contact with the spring on the...
3. First order ordinary differential equation) A solution containing 90% by volume of alcohol (in...
3. First order ordinary differential equation) A solution containing 90% by volume of alcohol (in water) runs at 1 liter per min into a 100-liter tank of pure water where it is continually mixed. The mixture is withdrawn at the rate of liter per min. The alcohol volume in the container, Nis given as AV-10 100 0515201 dr 10 We would like to predict the alcohol volume in the tank, N as a function time, t. Use At-1 s. Solve...
Problem Set A Problem 6. (20%) A ordinary differential equation for a mass-damper-spring system is following....
Problem Set A Problem 6. (20%) A ordinary differential equation for a mass-damper-spring system is following. The mass m 1, damping coetfic e initial position y(o) O, and the initial velocity i constant k 3 and force 10, all are in appropriate units. Th 1, spring zero, within the time range of O to 20 unit of time, use Matlab find the solution of function y(t)? Hint: you need to convert the 2nd order ODE into two 1st order ODEs....
In a decontamination plant, we have the following tank system:
a) Write the differential equation allowing to model the quantity of pollutant in the tank A and solve this differential equation.
b) Write the differential equation allowing to model the variation of the volume in the tank B.
c) Write the differential equation allowing to model the quantity of pollutant in the tank B and solve this differential equation.
d) When does the volume of tank B reach 200 liters?...
The position x of a mass m attached to a spring obeys the differential equation i + yi + w?x = 0 where y 2w. a) (2 marks) Write down expressions for the forces on the mass due to (i) the spring, and (ii) damping. (3 marks) Using a trial solution x = Ae"', show that a = --y/2 ± (y2/4 - «2)1/2 b) c) (4 marks) Show, by finding wd, that the solution is a damped oscillation of the...
Self Test 2 balance) (Unsteady State mass 1 Problem Statement A Vertical tank of diameter D and height H has a narrow crack of width W running vertically from top to bottom. If the tank is initially filled with water and alilowed to drain through the crack under the influence of gravity a) Calculate the output volumetric flow rate at any time t Imagine the crack to be a seties of adiacenr orifices, then, integrate to find the total efflux...
Please answer this problem FULLY with detail steps on how to
slove. My professor normally has us answer these questions by hand,
and for complex imformation to put the rest into Excel. So, the
handworked steps and solutions would be greatly apprecited. Thank
you!
For the following problems you must develop a diagram to show the situation, include a brief problem statement and clearly show the energy balance equations you are using (start from the appropriate form of the energy...
Self Test 2 (Unsteady State mass balance) 1. Problem Statement A Vertical tank of diameter D and height H has a narrow crack of width W running vertically from top to bottom. If the tank is initially filled with water and ailowed to drain through the crack under the influence of gravity; a) Calculate the output volumetric flow rate at any time t Imagine the crack to be a series of adjacent orifices, then, integrate to find the total efflux...
(a) The differential equation describing the motion of a stretched string 4. can be writ- ten y T Define the symbols that appear in this equation. [3 marks] (b) A uniform stretched string has length 2 m, mass 40 g and a fundamental fre- quency of 75 Hz. [4 marks] (i) Calculate the tension in the string. (ii) Write explicit expressions for the two lowest frequency normal modes of the string and sketch their shapes. (iii) The string is pulled...
Spring mass damper system with forced response, the forced system given by the equation For damping factor:E-0.1 ; mass; m-| kg: stiffness of spring; k-100 Nm; f-| 00 N; ω Zun; initial condition: x (0)-2 cms; r(0) = 0. fsincot Task Marks 1. Write down the reduced equation into 2first orderns Hand written equations differential equations 2. Rearrange equation (1) with the following generalized equation 250, x+osinor calculations 3. Calculate the value of c calculations Hand calculations 4. Using the...
Elementary Differential Equation Unit Step Function Problem
Project 2 A Spring-Mass Event Problenm A mass of magnitude m is confined to one-dimensional motion between two springs on a frictionless horizontal surface, as shown in Figure 4.P.3. The mass, which is unattached to either spring, undergoes simple inertial motion whenever the distance from the origin of the center point of the mass, x, satisfies lxl < L. When x 2 L, the mass is in contact with the spring on the...
3. First order ordinary differential equation) A solution containing 90% by volume of alcohol (in water) runs at 1 liter per min into a 100-liter tank of pure water where it is continually mixed. The mixture is withdrawn at the rate of liter per min. The alcohol volume in the container, Nis given as AV-10 100 0515201 dr 10 We would like to predict the alcohol volume in the tank, N as a function time, t. Use At-1 s. Solve...
Problem Set A Problem 6. (20%) A ordinary differential equation for a mass-damper-spring system is following. The mass m 1, damping coetfic e initial position y(o) O, and the initial velocity i constant k 3 and force 10, all are in appropriate units. Th 1, spring zero, within the time range of O to 20 unit of time, use Matlab find the solution of function y(t)? Hint: you need to convert the 2nd order ODE into two 1st order ODEs....
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