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alexdok [17]
3 years ago
14

A thick steel slab ( 7800 kg/m3, 480 J/kg·K, 50 W/m·K) is initially at 300°C and is cooled by water jets impinging on one of its

surfaces. The temperature of the water is 25°C, and the jets maintain an extremely large, approximately uniform convection coefficient at the surface. Assuming that the surface is maintained at the temperature of the water throughout the cooling, how long will it take for the temperature to reach 50°C at a distance of 30 mm from the surface?

Engineering
2 answers:
AleksandrR [38]3 years ago
4 0

Answer: 67.392s

Explanation: detailed calculation is shown below

dlinn [17]3 years ago
3 0

Answer:

Time(t) = 2592.91 seconds

Explanation:

From the question, we have;

ρ = 7800 kg/m

c =480 J/kg⋅K

k = 50 W/m⋅K

Ti = 300°C

Ts = 25°C

x = 25 mm or in meters; = 0.025 m

From formula, we know that;

(T(x,t) - T(s))/(T(i) - T(s)) = erf(x/(2√(αt))

Where erf is error function

And α = k/(ρc)

So, solving we have;

(50 - 25)/(300 - 25) = erf(x/(2√(αt))

erf(x/(2√(αt)) = 0.0909

From the error function table which i attached, 0.0909 will give us approximately 0.0806 upon interpolation.

Thus, (x/(2√(αt)) = 0.0806

Let's make "t" the subject of the formula;

x² = 0.0806²(2²)(αt)

t = x²/0.026α

Let's find α

From earlier, we saw that;

α = k/(ρc)

Thus; α = 50/(7800 x 480) = 1.335 x 10^(-5) m²/s

Also, from the question, x = 30mm or 0.03m

So, t = 0.03²/(0.026 x 1.335 x 10^(-5)) = 2592.91 seconds

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3 years ago
A 4-kW electric heater runs for 2 hours to raise the room temperature to the desired level. Determine the amount of electric ene
Anna35 [415]

Answer:

Q' = 8 KW.h

Q'=28800 KJ

Explanation:

Given that

Heat Q= 4 KW

time ,t = 2 hours

The amount of energy used in KWh given as

Q ' = Q x t

Q' = 4 x  2 KW.h

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We know that W  = 1 J/s

The amount of energy used in KJ given as

Q' = 8 x 3600 = 28800 KJ

Therefore

Q' = 8 KW.h

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6 0
3 years ago
If a system of pulleys results in a force of 25% of the load, how far will the rope need to move to pull the load a distance of
GaryK [48]

Answer:

  40 ft

Explanation:

Assuming no loss of energy in the system of pulleys, the work done is the same whether you move the load directly or through the pulleys.

  W = Fd . . . . . . . . work is the product of force and distance

  F(10 ft) = (0.25F)(d) . . . . . where d is the distance we want to find

  d = 10F/(0.25F) = 40

The rope will need to move 40 feet.

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2 years ago
Use the Hurricanes data and via Multiple regression select the three input variables: Min-pressure, Gender, Category in order to
S_A_V [24]

Answer:

Answer for the question:

Use the Hurricanes data and via Multiple regression select the three input variables: Min-pressure, Gender, Category in order to predict the All-Deaths. Pick one of the three variables that has the best P-value and re-do the regression using ONLY this one variable to predict the All-deaths. Answer the questions. (Numerical answers are rounded so choose the answer that matches the best).

is explained in the attachment.

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6 0
3 years ago
The motor of an electric vehicle runs at an average of 50 hp for one hour and 25 minutes. Determine the total energy. Write the
Sunny_sXe [5.5K]

Answer:

The total energy of the motor of the electric vehicle is 1.902 × 10⁸ joules.

Explanation:

Power is the rate of change of work in time, since given input is average power, the total energy (\Delta E) of the motor of the electric vehicle, measured in joules, is determined by this formula:

\Delta E = \dot W \cdot \Delta t

Where:

\dot W - Average power, measured in watts.

\Delta t - Time, measured in seconds.

Now, let convert average power and time into watts and seconds, respectively:

Average Power

\dot W = (50\,hp)\times \frac{746\,W}{1\,hp}

\dot W = 3.730\times 10^{4}\,W

Time

\Delta t = (1\,h)\times \frac{3600\,s}{1\,h} + (25\,min)\times \frac{60\,s}{1\,min}

\Delta t = 5.100\times 10^{3}\,s

Then, the total energy is:

\Delta E = (3.730\times 10^{4}\,W)\cdot (5.100\times 10^{3}\,s)

\Delta E = 1.902\times 10^{8}\,J

The total energy of the motor of the electric vehicle is 1.902 × 10⁸ joules.

6 0
3 years ago
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