A swimmingpool have the volume 1000 m3. With the time t = 0, the swimmingpool is empty. We fill in so much water into the swimmingpool with constant speed v = 2,4 m3 per minute. At the same time, it is leaking water out of the swimmingpool simultaneous and the speed is at every moment proportional with the volume of the water. The proportional constant is a = 3*10-3minute-1
a) make a differential equation as V(t) have to satisfy.
b) solve the solution with the method with integral factor.
c) find out when the swimmingpool is half full.
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A swimmingpool have the volume 1000 m3. With the time
t = 0, the swimmingpool is...
A pool has a volume of 1000 ?3. At time ? = 0 the pool is...
A pool has a volume of 1000 ?3. At time ? = 0 the pool is empty. We then fill in water the pool at a constant speed ? = 2.4?3 per minute. At the same time, water is leaking out the pool at a rate that is at all times proportional to the volume of water. The proportionality constant is ? = 3 ∙ 10−3??nute-1. Let ? (?) be the volume of water in the pool t minutes after...
A rectangular box of height h metres with a square base with side x(t) metres, where initial leng...
A rectangular box of height h metres with a square base with side x(t) metres, where initial length of the side of the base is x(0) 2 metres. The box is initially filled with water to a height of h(0) - 4 metres. The volume of water is given by V-(t)h(t) Over time, the sides of the base are decreasing at a rate of dt =-0.05 m/s and the water is leaking from a hole in the base of the...
7.2.6 A swimming pool has a volume of 50 m. A mass C (in kg) of chlorine is dissolved in the pool water. Starting at a time 0, water containing a con- centration of 0.1 C/V chlorine is pumped in...
7.2.6 A swimming pool has a volume of 50 m. A mass C (in kg) of chlorine is dissolved in the pool water. Starting at a time 0, water containing a con- centration of 0.1 C/V chlorine is pumped into the swimming pool at a rate of 0.02 m3/min, and the water flows out at the same rate. a) Present the differential equation for the chlorine mass O). b) Find the solution O(t) to this equation. c) What is the...
(25 pts) We have a tank of volume V which contains an ideal gas at constant temperature T and initial pressure Po. There is a small hole in the tank and gas leaks out at a velocity of (RT)5, We c...
(25 pts) We have a tank of volume V which contains an ideal gas at constant temperature T and initial pressure Po. There is a small hole in the tank and gas leaks out at a velocity of (RT)5, We can use a molar density 1. Recall that mols in tanke ρν and molar rate out-pud where u-velocity and A - area of hole. Derive the differential equation for P vs t (hint it's a simple exponential) a. drop in...
Point) For this problem, time is given by the variable t, position by s, area by A, and volume by...
I want correct answer
point) For this problem, time is given by the variable t, position by s, area by A, and volume by V. Numerical an swers require Translate the following sentences into Leibniz notation: (a) The position of an object is increasing at a rate of 25 meters per second ds 25m/s dt (b) The area of an object is increasing by 14 square meters every minute dA ...14mA2 dt (c) The volume of an object is decreasing...
DE the score for the find (25 pts) We have a tank of volume V which contains an ideal gas at constant temperature T and initial pressure Po. There is a small hole in the tank and gas leaks...
DE the score for the find (25 pts) We have a tank of volume V which contains an ideal gas at constant temperature T and initial pressure Po. There is a small hole in the tank and gas leaks out at a velocity of (RT)05. We can use a molar density of p T ocity and molar rate out - puA where u - vel Recall that mols in tank- pV and A = area of hole. Derive the differential...
this is differential equations practice problem part d should be t = 0, thank you in...
this is differential equations practice problem
part d should be t = 0,
thank you in sdvancdd!
1. An object of mass m is fired vertically upward with an initial speed of vo. Suppose the air resistance is proportional to the square of velocity. Let k > O be the constant of proportionality. Use g as the acceleration due to gravity. Let v(t) be the velocity at time t. a) Write down the differential equation in effect for v(t) until...
quality x=0.5 indicates a liquid/vapor mix. A piston cylinder device contains V-0 2 m3 of water...
quality x=0.5 indicates a liquid/vapor mix.
A piston cylinder device contains V-0 2 m3 of water at P 140 kPa and a quality of x/=0.5. The cross- sectional area of the piston is A-0.2 m2 and is restrained by a linear spring with spring constant K-52 kN/m Heat is added to the water until the volume expands to V2= 0.4 m3 (a) Determine the mass of water and the final pressure P2 (b) Fill in all other missing properties in...
2. An object of 5 kg is released from rest 1000 meters above the ground level...
2. An object of 5 kg is released from rest 1000 meters above the ground level and allowed to fall under the influence of gravity. Assuming that the force due to air resistance is proportional to the velocity of the object with proportionality constant k = 50 kg/sec determine the formula for the velocity of the object 3. A rocket having an initial mass mo kg is launched vertically from the surface of the Earth. The rocket expels gas at...
The flow system shown in the figure is activated at time t = 0. Let Qi(t)...
The flow system shown in the figure is activated at time t = 0. Let Qi(t) denote the amount of solute present in the ith tank at time t. Assume that all the flow rates are a constant 10 L/min. It follows that the volume of solution in each tank remains constant; assume this volume to be 1000 L. The concentration of solute in the inflow to Tank 1 (from a source other than Tank 2) is 0.2 kg/L, and...
A rectangular box of height h metres with a square base with side x(t) metres, where initial length of the side of the base is x(0) 2 metres. The box is initially filled with water to a height of h(0) - 4 metres. The volume of water is given by V-(t)h(t) Over time, the sides of the base are decreasing at a rate of dt =-0.05 m/s and the water is leaking from a hole in the base of the...
7.2.6 A swimming pool has a volume of 50 m. A mass C (in kg) of chlorine is dissolved in the pool water. Starting at a time 0, water containing a con- centration of 0.1 C/V chlorine is pumped into the swimming pool at a rate of 0.02 m3/min, and the water flows out at the same rate. a) Present the differential equation for the chlorine mass O). b) Find the solution O(t) to this equation. c) What is the...
(25 pts) We have a tank of volume V which contains an ideal gas at constant temperature T and initial pressure Po. There is a small hole in the tank and gas leaks out at a velocity of (RT)5, We can use a molar density 1. Recall that mols in tanke ρν and molar rate out-pud where u-velocity and A - area of hole. Derive the differential equation for P vs t (hint it's a simple exponential) a. drop in...
I want correct answer
point) For this problem, time is given by the variable t, position by s, area by A, and volume by V. Numerical an swers require Translate the following sentences into Leibniz notation: (a) The position of an object is increasing at a rate of 25 meters per second ds 25m/s dt (b) The area of an object is increasing by 14 square meters every minute dA ...14mA2 dt (c) The volume of an object is decreasing...
DE the score for the find (25 pts) We have a tank of volume V which contains an ideal gas at constant temperature T and initial pressure Po. There is a small hole in the tank and gas leaks out at a velocity of (RT)05. We can use a molar density of p T ocity and molar rate out - puA where u - vel Recall that mols in tank- pV and A = area of hole. Derive the differential...
this is differential equations practice problem
part d should be t = 0,
thank you in sdvancdd!
1. An object of mass m is fired vertically upward with an initial speed of vo. Suppose the air resistance is proportional to the square of velocity. Let k > O be the constant of proportionality. Use g as the acceleration due to gravity. Let v(t) be the velocity at time t. a) Write down the differential equation in effect for v(t) until...
quality x=0.5 indicates a liquid/vapor mix.
A piston cylinder device contains V-0 2 m3 of water at P 140 kPa and a quality of x/=0.5. The cross- sectional area of the piston is A-0.2 m2 and is restrained by a linear spring with spring constant K-52 kN/m Heat is added to the water until the volume expands to V2= 0.4 m3 (a) Determine the mass of water and the final pressure P2 (b) Fill in all other missing properties in...
2. An object of 5 kg is released from rest 1000 meters above the ground level and allowed to fall under the influence of gravity. Assuming that the force due to air resistance is proportional to the velocity of the object with proportionality constant k = 50 kg/sec determine the formula for the velocity of the object 3. A rocket having an initial mass mo kg is launched vertically from the surface of the Earth. The rocket expels gas at...
The flow system shown in the figure is activated at time t = 0. Let Qi(t) denote the amount of solute present in the ith tank at time t. Assume that all the flow rates are a constant 10 L/min. It follows that the volume of solution in each tank remains constant; assume this volume to be 1000 L. The concentration of solute in the inflow to Tank 1 (from a source other than Tank 2) is 0.2 kg/L, and...
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