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shepuryov [24]
3 years ago
8

g A circular oil slick of uniform thickness is caused by a spill of one cubic meter of oil. The thickness of the oil slick is de

creasing at a rate of 0.1 centimeters per hour. At what rate is the radius of the slick increasing when the radius is 8 meters?
Engineering
1 answer:
Anika [276]3 years ago
4 0

Answer:

the rate of increase of radius is dR/dt = 0.804 m/hour = 80.4 cm/hour

Explanation:

the slick of oil can be modelled as a cylinder of radius R and thickness h, therefore the volume V is

V = πR² * h

thus

h = V / (πR²)

Considering that the volume of the slick remains constant, the rate of change of radius will be

dh/dt = V d[1/(πR²)]/dt

dh/dt = (V/π) (-2)/R³ *dR/dt

therefore

dR/dt = (-dh/dt)* (R³/2) * (π/V)

where dR/dt = rate of increase of the radius , (-dh/dt)= rate of decrease of thickness

when the radius is R=8 m , dR/dt is

dR/dt = (-dh/dt)* (R³/2) * (π/V) = 0.1 cm/hour *(8m)³/2 * π/1m³ *(1m/100 cm)= 0.804 m/hour = 80.4 cm/hour

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Ann [662]

Answer:

Hr=4.2*10^7\ btu/hr

Explanation:

From the question we are told that:

Water flow Rate R=4.5slug/s=144.78ib/sec

Initial Temperature T_1=60 \textdegree F

Final Temperature  T_2=140 \textdegree F

Let

Specific heat of water \gamma= 1

And

 \triangle T= 140-60

 \triangle T= 80\ Deg.F

Generally the equation for Heat transfer rate of water  H_r is mathematically given by

Heat transfer rate to water= mass flow rate* specific heat* change in temperature

 H_r=R* \gamma*\triangle T

 H_r=144.78*80*1

 H_r=11582.4\ btu/sec

Therefore

 H_r=11582.4\ btu/sec*3600

 Hr=4.2*10^7\  btu/hr

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3 years ago
Please define the coefficient of thermal expansion?
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Answer:

The coefficient of thermal expansion tells us how much a material can expand due to heat.

Explanation:

Thermal expansion occurs when a material is subjected to heat and changes it's shape, area and volume as a result of that heat. How much that material changes is dependent on it's coefficient of thermal expansion.

Different materials have different coefficients of thermal expansion (i.e. It is a material property and differs from one material to the next). It is important to understand how materials behave when heated, especially for engineering applications when a change in dimension might pose a problem or risk (eg. building large structures).

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Select the creative imaging fields that require knowledge of programming.
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Video game designer for sure
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One who waits too long to complain has indicated satisfaction with the agreement despite the initial lack of true consent is the
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Answer: Doctrine of ratification

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3 years ago
Gear A has a mass of 1 kg and a radius of gyration of 30 mm; gear B has a mass of 4 kg and a radius of gyration of 75 mm; gear C
Kruka [31]

Answer:

(4.5125 * 10^-3 kg.m^2)ω_A^2

Explanation:

solution:

Moments of inertia:

I = mk^2

Gear A: I_A = (1)(0.030 m)^2 = 0.9*10^-3 kg.m^2

Gear B: I_B = (4)(0.075 m)^2 = 22.5*10^-3 kg.m^2

Gear C: I_C = (9)(0.100 m)^2 = 90*10^-3 kg.m^2

Let r_A be the radius of gear A, r_1 the outer radius of gear B, r_2 the inner radius of gear B, and r_C the radius of gear C.

r_A=50 mm

r_1 =100 mm

r_2 =50 mm

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At the contact point between gears A and B,

r_1*ω_b = r_A*ω_A

ω_b = r_A/r_1*ω_A

       = 0.5ω_A

At the contact point between gear B and C.

At the contact point between gears A and B,

r_C*ω_C = r_2*ω_B

ω_C = r_2/r_C*ω_B

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kinetic energy T = 1/2*I_A*ω_A^2+1/2*I_B*ω_B^2+1/2*I_C*ω_C^2

                           =(4.5125 * 10^-3 kg.m^2)ω_A^2

6 0
3 years ago
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