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Sati [7]
2 years ago
11

The volume of a cylinder is to be determined from measurements of the diameter and length. If the length and diameter are measur

ed at four different locations by means of a micrometer with an uncertainty of 0.5% of reading, determine the uncertainty in the measurement.
Engineering
1 answer:
sveta [45]2 years ago
5 0

Answer: The uncertainty in the measurements is 4%

Explanation: uncertainty is the doubt or level of not being sure about an outcome or a result.

Because the volume of the cylinder is gotten by measuring length and diameter of the cylinder, using a micrometer that has a 0.5% uncertainty, this will cause the measurements of each value to have a 0.5% uncertainty.

Therefore, since the length has 0.5% uncertainty and the diameter has 0.5% uncertainty too.

The uncertainty in the measurement will be.

0.5% + 0.5% = 1%

Since we are told that this measurement was carried out in four different locations, that means the uncertainty will become;

1% × 4 = 4%

As the number of locations increases, the uncertainty in the measurement will increase as well.

You might be interested in
A plate of an alloy steel has a plane-strain fracture toughness of 50 MPa√m. If it is known that the largest surface crack is 0.
Ivahew [28]

Answer:

option B is correct. Fracture will definitely not occur

Explanation:

The formula for fracture toughness is given by;

K_ic = σY√πa

Where,

σ is the applied stress

Y is the dimensionless parameter

a is the crack length.

Let's make σ the subject

So,

σ = [K_ic/Y√πa]

Plugging in the relevant values;

σ = [50/(1.1√π*(0.5 x 10^(-3))]

σ = 1147 MPa

Thus, the material can withstand a stress of 1147 MPa

So, if tensile stress of 1000 MPa is applied, fracture will not occur because the material can withstand a higher stress of 1147 MPa before it fractures. So option B is correct.

8 0
2 years ago
Water (cp = 4180 J/kg·°C) enters the 2.5 cm internal diameter tube of a double-pipe counter-flow heat exchanger at 17°C at a rat
aksik [14]

Answer:

Length = 129.55m, 129.55m

Explanation:

Given:

cp of water = 4180 J/kg·°C

Diameter, D = 2.5 cm

Temperature of water in =  17°C

Temperature of water out = 80°C

mass rate of water =1.8 kg/s.

Steam condensing at 120°C

Temperature at saturation = 120°C

hfg of steam at 120°C = 2203 kJ/kg

overall heat transfer coefficient of the heat exchanger = 700 W/m2 ·°C

U = 700 W/m2 ·°C

Since Temperature of steam is at saturation,

temperature of steam going in = temperature of steam out = 120°C

Energy balance:

Heat gained by water = Heat loss by steam

Let specific capacity of steam = 2010kJ/Kg .°C

Find attached the full solution to the question.

3 0
2 years ago
The 30-kg gear is subjected to a force of P=(20t)N where t is in seconds. Determine the angular velocity of the gear at t=4s sta
tatyana61 [14]

Answer:

\omega =\frac{24}{1.14375}=20.983\frac{rad}{s}

Explanation:

Previous concepts

Angular momentum. If we consider a particle of mass m, with velocity v, moving under the influence of a force F. The angular  momentum about point O is defined as the “moment” of the particle’s linear momentum, L, about O. And the correct formula is:

H_o =r x mv=rxL

Applying Newton’s second law to the right hand side of the above equation, we have that r ×ma = r ×F =

MO, where MO is the moment of the force F about point O. The equation expressing the rate of change  of angular momentum is this one:

MO = H˙ O

Principle of Angular Impulse and Momentum

The equation MO = H˙ O gives us the instantaneous relation between the moment and the time rate of change of angular  momentum. Imagine now that the force considered acts on a particle between time t1 and time t2. The equation MO = H˙ O can then be integrated in time to obtain this:

\int_{t_1}^{t_2}M_O dt = \int_{t_1}^{t_2}H_O dt=H_0t2 -H_0t1

Solution to the problem

For this case we can use the principle of angular impulse and momentum that states "The mass moment of inertia of a gear about its mass center is I_o =mK^2_o =30kg(0.125m)^2 =0.46875 kgm^2".

If we analyze the staritning point we see that the initial velocity can be founded like this:

v_o =\omega r_{OIC}=\omega (0.15m)

And if we look the figure attached we can use the point A as a reference to calculate the angular impulse and momentum equation, like this:

H_Ai +\sum \int_{t_i}^{t_f} M_A dt =H_Af

0+\sum \int_{0}^{4} 20t (0.15m) dt =0.46875 \omega + 30kg[\omega(0.15m)](0.15m)

And if we integrate the left part and we simplify the right part we have

1.5(4^2)-1.5(0^2) = 0.46875\omega +0.675\omega=1.14375\omega

And if we solve for \omega we got:

\omega =\frac{24}{1.14375}=20.983\frac{rad}{s}

8 0
2 years ago
6. You are an electrician working in an industrial plant. You are building a motor control cabinet that contains six motor start
Sveta_85 [38]

Answer:

It's indeed safer to suggest a 150 VA transformer. Following table however is the clarification given.

Explanation:

For 2 motors with 0.1 A, the Power will be:

P = 2\times 120\times 0.1

  = 24 \ W

For 4 motors with 0.18 A, the Power will be:

P = 4\times 120\times 0.18

  = 86.4 \ W

As we know, for 6 pilot lamps, the power is "5 W".

So,

The total power will be:

⇒ P = 24+86.4+5

       = 115.4 \ W

Now,

Consider the power factor to be "0.95"

VA of transformer is:

= PF\times Power

= 115.4\times 0.9

= 109.63 \ VA

8 0
2 years ago
Consider film condensation on a vertical plate. Will the heat flux be higher at the top or at the bottom of the plate? Why?
STALIN [3.7K]

Answer:

During film condensation on a vertical plate, heat flux at the top will be higher since the thickness of the film at the top, and thus its thermal resistance, is lower.

Explanation:

https://www.docsity.com/pt/cengel-solution-heat-and-mass-transfer-2th-ed-heat-chap10-034/4868218/

https://arc.aiaa.org/doi/pdf/10.2514/1.43136

https://arxiv.org/ftp/arxiv/papers/1402/1402.5018.pdf

8 0
2 years ago
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