Suppose:• The vat contains 230 gallons of liquid, which never changes.• Sugar water with a concentration of 7 tablespoons/gallon flows through pipe A into the vat at therate of 5 gallons/minute.●Sugar water with a concentration of 3 tablespoons/gallon flows through pipe B into the vat at therate of 25 gallons/minute.• The liquid in the vat is kept well-mixed.• Sugar water leaves the vat through pipe C at the rate of 30 gallons/minute.Let S(t) represent the number of tablespoons of sugar in the vat at time t, where t is given in minutes.(A) Write the DE model for the time rate of change of sugar in the vat:dS2530-3523Xdt(B) Solve the differential equation to find the amount of sugar in the vat as a function of time. Yourfunction will have an arbitrary constant K in it. Assume that K > 0.S(t)= 250- KeX(C) Suppose that there are 22 tablespoons of sugar in the vat at t = 0. How many tablespoons will bepresent 2 minutes later?42x tablespoonsO# 33с14$%6&877O*O✔C Consider a large vat containing sugar water that is to be made into soft drinks (see figure below).ABSuppose:• The vat contains 230 gallons of liquid, which never changes.• Sugar water with a concentration of 7 tablespoons/gallon flows through pipe A into the vat at therate of 5 gallons/minute.• Sugar water with a concentration of 3 tablespoons/gallon flows through pipe B into the vat at therate of 25 gallons/minute.• The liquid in the vat is kept well-mixed.Sugar water leaves the vat through pipe C at the rate of 30 gallons/minute.Let S(t) represent the number of tablespoons of sugar in the vat at time t, where t is given in minutes.(A) Write the DE model for the time rate of change of sugar in the vat:dS2530-3523Xdt(B) Solve the differential equation to find the amount of sugar in the vat as a function of time. Yourfunction will have an arbitrary constant K in it. Assume that K > 0.S(t)= 250- KeX(C) Suppose that there are 22 tablespoons of sugar in the vat at t = 0. How many tablespoons will bepresent 2 minutes later?M

Introduction: In this issue, we will determine the rate of change of sugar in the vat while sugar…

C Suppose: • The vat contains 230 gallons of liquid, which never changes. ● Sugar water with a concentration of 7 tablespoons/gallon flows through pipe A into the vat at the rate of 5 gallons/minute. • Sugar water with a concentration of 3 tablespoons/gallon flows through pipe B into the vat at the rate of 25 gallons/minute. • The liquid in the vat is kept well-mixed. • Sugar water leaves the vat through pipe C at the rate of 30 gallons/minute.

C Suppose: • The vat contains 230 gallons of liquid, which never changes. ● Sugar water with a concentration of 7 tablespoons/gallon flows through pipe A into the vat at the rate of 5 gallons/minute. • Sugar water with a concentration of 3 tablespoons/gallon flows through pipe B into the vat at the rate of 25 gallons/minute. • The liquid in the vat is kept well-mixed. • Sugar water leaves the vat through pipe C at the rate of 30 gallons/minute.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Fluid Dynamics

The study of the flow of gases and liquids, usually in and around solid surfaces, is known as fluid dynamics in physics and engineering. Fluid dynamics, for example, can be used to evaluate the movement of air through an airplane wing or the surface of a vehicle. It can also be used in ship design to increase the speed at which ships pass through water.

Question

Suppose:
• The vat contains 230 gallons of liquid, which never changes.
• Sugar water with a concentration of 7 tablespoons/gallon flows through pipe A into the vat at the
rate of 5 gallons/minute.
●
Sugar water with a concentration of 3 tablespoons/gallon flows through pipe B into the vat at the
rate of 25 gallons/minute.
• The liquid in the vat is kept well-mixed.
• Sugar water leaves the vat through pipe C at the rate of 30 gallons/minute.
Let S(t) represent the number of tablespoons of sugar in the vat at time t, where t is given in minutes.
(A) Write the DE model for the time rate of change of sugar in the vat:
dS
2530-35
23
X
dt
(B) Solve the differential equation to find the amount of sugar in the vat as a function of time. Your
function will have an arbitrary constant K in it. Assume that K > 0.
S(t)= 250- Ke
X
(C) Suppose that there are 22 tablespoons of sugar in the vat at t = 0. How many tablespoons will be
present 2 minutes later?
42
x tablespoons
O
# 3
3
с
14
$
%
6
&
87
7
O
*
O
✔
C

Consider a large vat containing sugar water that is to be made into soft drinks (see figure below).
A
B
Suppose:
• The vat contains 230 gallons of liquid, which never changes.
• Sugar water with a concentration of 7 tablespoons/gallon flows through pipe A into the vat at the
rate of 5 gallons/minute.
• Sugar water with a concentration of 3 tablespoons/gallon flows through pipe B into the vat at the
rate of 25 gallons/minute.
• The liquid in the vat is kept well-mixed.
Sugar water leaves the vat through pipe C at the rate of 30 gallons/minute.
Let S(t) represent the number of tablespoons of sugar in the vat at time t, where t is given in minutes.
(A) Write the DE model for the time rate of change of sugar in the vat:
dS
2530-35
23
X
dt
(B) Solve the differential equation to find the amount of sugar in the vat as a function of time. Your
function will have an arbitrary constant K in it. Assume that K > 0.
S(t)= 250- Ke
X
(C) Suppose that there are 22 tablespoons of sugar in the vat at t = 0. How many tablespoons will be
present 2 minutes later?
M

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... Moving to another question will save this response. Question 7 Compressed air with a flowrate of 8 kg/min flows through a two-stage turbine and heat exchanger system as follows: • At the entrance to the system (point 1), the pressure of the air is 8 bar and the temperature of the air is 359 K. • From 1-2 the air passes through a heat exchanger which increases its temperature to 922 K. • From 2-3 the air passes through a turbine, with a pressure ratio of 3 (i.e. P₂/p₂=3). This first turbine has an isentropic efficiency of 65%. • From 3-4 the air passes through a second heat exchanger, which increases its temperature back up to 922 K. • From 4-5 the air passes through a second turbine with a pressure ratio of 3 and an isentropic efficiency of 80%. The properties of air are: cp = 1.005 kJ/kgk, cv = 0.718 kJ/kgK, R = 0.287 kJ/kgK, and y= 1.4. Select the correct value for each of the following values: ₂) a. The heat transfer to the air in the first heat exchanger (i.e. ₁) i in kW: b.…
Please show system sketches and related energy flows for all problems. 1.1 Determine the electrical power supplied to a boiler when the temperature of the entering water is 20 C and the exiting temperature is 89 C. The flow of the pressured water is 2 Kg/s. There is a negligible pressure drop through this boiler and it operates at a constant pressure of 3 bars. The specific heat is c = 4,370 J/(Kg K). There is a 1.5(105 ) W rate of heat loss from the boiler during this process to a surrounding at 293.2 k. Consider steady state conditions. 1.4 Calculate the mass flowrate of fuel (natural gas, CH4) required to heat the water flow to the conditions of problem 1.1 if the electrical heating device is replaced with a gas fired boiler. The high heating value (HHV) of the fuel is 50.02 MJ/kg. 1.5 Calculate the exergy destroyed in the process described by problem 1.4. The exergy of the fuel entering this process is 51.82 MJ/Kg. The dead state temperature is 293.2 K and pressure is 1 bar. The…
Question 2. Solve with detailed solutions please. Thank You
Q 13 please
b) A tank shown in Figure-2 below is used to mix methanol and salt. The tank initially contains 1 m³ of methanol. Salt is provided into the tank with a volumetric flow rate of Fsalt= 0.2 m³ s¹. A stream with perfectly mixed methanol and salt leaves the tank with a volumetric flow rate of F = 0.1 m³ s1. As the flow is unsteady, the volume of mixture in the tank, V(t), is a function of time. Fsalt=0.2 m³/s Psalt=2160 kg/m³ V(t) F=0.1 m³/s Figure-2: A mixing tank of methanol and salt. d(V (t)Psalt) dt Salt+methanol The mass balance of salt in the tank is given by, d(V (t) (Psalt +Pmethanol)) dt = Fsalt Psalt - FPsalt where Psalt is the density of salt and equal to 2160 kgm ³. The total mass in the tank is given by, = Fsalt Psalt - FPsalt - FPmethanol where Pmethanol is the density of methanol and equal to 800 kgm-³. When the tank contains V = 0.5m³ of mixture, what is the mass of salt in the tank? Use the explicit Euler finite difference method to discretise the balance equations. (Hint:…
a.) Determine the mass flow rate of the water vapor, in kg/hr.b.) Calculate the volumetric flow rate of the water vapor leaving the plant, in m^3/hr.c.) Calculate the volumetric flow rate of the brine, in m^3/hr.
Waste from a copper plating facility is being discharged into a receiving stream. The waste stream contains 3.5 mg/L copper with a flow of 4.0 x106 L/day. The receiving stream has an upstream flow of 2.6x107 L/day and 0.50 mg/L of copper. Assume complete and instantaneous mixing at the point where the streams meet and that the system is at steady state. a) Draw the stream disgram b) What is the copper concentration in mg/L immediately downstream of the copper plating facility? c) How many kg per day are contributed to the receiving stream by the copper plating facility? d) What percentage of all of the copper mass in the downstream water is contributed by the upstream flow?