1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
dangina [55]
3 years ago
12

A 3-phase induction motor with 4 poles is being driven at 45 Hz and is running in its normal operating range. When connected to

a certain load, the motor rotates at a speed of 1070 rpm and outputs 800W a. What is the slip and developed torque? b. What is the new slip and motor speed if the developed torque is reduced to 4 Nm?
Engineering
1 answer:
Dennis_Churaev [7]3 years ago
5 0

Answer:

a) The slip for the given conditions is 0.2074 or 20.74% and the developed torque is 7.14 Nm.

b) The new slip after reducing the torque to 4 Nm is 0.1162 or 11.62% and the new motor speed is 1193.13 rpm.

Explanation:

In order to find the slip we can use the definition as the relative difference between Synchronous speed and the rotor speed and that the developed torque is the ratio between output power and rotor angular velocity.

Slip.

We can find the synchronous speed u sing the following formula

N_s =\cfrac{120f}p

Where f stands for the frequency and p the number of poles, so we have

N_s = \cfrac{120(45)}{4}\\N_s =1350 \,rpm

Replacing on the slip formula

S = \cfrac{N_s-N_r}{N_s}

we get

S = \cfrac{1350-1070}{1350}\\ S = 0.2074

Thus the slip for the given conditions is 0.2074 or 20.74%.

Developed torque.

We can find the angular velocity in radians per second

\omega_r =1070  \cfrac{rev}{min} \times \cfrac{1 \, min}{60 \, s}\times \cfrac{2\pi rad}{1 \, rev}\\\omega_r =112.05 \, \cfrac{rad}{s}

Thus we can replace on the torque formula

\tau = \cfrac{P}{\omega_r}\\\tau=\cfrac{800 W}{112.05 \, \cfrac{rad}{s}}

We get

\tau = 7.14\,  N m

The developed torque is 7.14 Nm.

Slip for the reduced torque.

The torque is proportional to the slip, so we can write

\cfrac{\tau_1}{\tau_2}= \cfrac{S_1}{S_2}

Thus solving for the new slip S_2 we have:

S_2 = S_1 \cfrac{\tau_2}{\tau_1}

Replacing the values obtained on the previous part we have

S_2 = 0.2074 \cfrac{4 Nm}{7.14 Nm}\\ S_2=0.1162

So the new slip after reducing the torque to 4 Nm is 0.1162 or 11.62%

Motor speed.

We can use the slip definition

S_2 =\cfrac{N_s-N_{r_2}}{N_s}

Solving for the motor speed we have

S_2N_s =N_s-N_{r_2}

N_{r_2}=N_s-S_2N_s \\N_{r_2}=N_s(1-S_2)

Replacing values we have

N_{r_2}=1350 \, rpm(1-0.1162)\\N_{r_2}=1193.13 rpm

The new motor speed is 1193.13 rpm.

You might be interested in
You have just finished your OST takeoffs for a single-story home and found 175 LF of interior walls with 2x6 studs 14" OC. The h
zimovet [89]

Answer:

Total BF for the interior wall is 7.50BD

Explanation:

Given Data:

· Size of stud = 2” x 6”

· Height of Wall = 8 ft

· Top plates = 2

· Bottom Plate = 1

BF stands for board feet in lumber/wood terminology. It is the unit of volume.

1 BF (Board feet) = 1 ft x 1 ft x 1 inch

Since there are total three plates at top and bottom, we have to deduct their thickness from wall height to calculate height of stud.

Height of stud = 8’ – 3 x 2” = 7’6” = 7.5 ft

Board feet of one stud = 7.50 6/12 x 2 = 7.50 BD

Total BF for the interior wall is 7.50BD

7 0
3 years ago
Close to 16 billion pounds of ethylene glycol (EG) were produced in 2013. It previously ranked as the twenty-sixth most produced
bekas [8.4K]

Answer:

a) 0.684

b) 0.90

Explanation:

Catalyst

EO + W → EG

<u>a) calculate the conversion exiting the first reactor </u>

CAo = 16.1 / 2   mol/dm^3

Given that there are two stream one  contains 16.1 mol/dm^3 while the other contains   0.9 wt% catalyst

Vo = 7.24 dm^3/s

Vm = 800 gal = 3028 dm^3

hence Im = Vin/ Vo = (3028 dm^3) / (7.24dm^3/s) = 418.232 secs = 6.97 mins

next determine the value of conversion exiting the reactor ( Xai ) using the relation below

KIm = \frac{Xai}{1-Xai}  ------ ( 1 )

make Xai subject of the relation

Xai = KIm / 1 + KIm  ---  ( 2 )

<em>where : K = 0.311 ,  Im = 6.97   ( input values into equation 2 )</em>

Xai = 0.684

<u>B) calculate the conversion exiting the second reactor</u>

CA1 = CA0 ( 1 - Xai )

therefore CA1 = 2.5438 mol/dm^3

Vo = 7.24 dm^3/s

To determine the value of the conversion exiting the second reactor  ( Xa2 ) we will use the relation below

XA2 = ( Xai + Im K ) / ( Im K + 1 ) ----- ( 3 )

<em> where : Xai = 0.684 , Im = 6.97,  and K = 0.311  ( input values into equation 3 )</em>

XA2 = 0.90

<u />

<u />

<u />

4 0
3 years ago
The 10 foot wide circle quarter gate AB is articulated at A. Determine the contact force between the gate and the smooth surface
slamgirl [31]

Answer:

F = 641,771.52 \dfrac{lb-ft}{s^2}

Explanation:

Given that

R=8 ft

Width= 10 ft

We know that hydro statics force given as

  F=ρ g A X

ρ is the density of fluid

A projected area on vertical plane

X is distance of center mass of projected plane from free surface of water.

Here

X=8/2  ⇒X=4 ft

A=8 x 10=80  ft^2

So now putting the values

F=ρ g A X

F=62.4(32.14)(80)(4)

F = 641,771.52 \dfrac{lb-ft}{s^2}

   

4 0
3 years ago
Which statement most accurately describes Pascal's law?
marin [14]

Answer:

La  C

Explanation:

7 0
3 years ago
Read 2 more answers
A 11.5 nC charge is at x = 0cm and a -1.2 nC charge is at x = 3 cm ..At what position or positions on the x-axis is the electric
diamong [38]

Answer:

Explanation:

Given

q_1=11.5\ nC charge is placed at x=0\ cm

another charge of q_2=-1.2\ nC is at x=3\ cm

We know that Electric field due to positive charge is away  from it and Electric field due to negative charge is towards it.

so net electric field is zero somewhere beyond negatively charged particle

Electric Field due to q_2 at some distance r from it

E_2=\frac{kq_2}{r^2}

Now Electric Field due to q_1 is

E_1=\frac{kq_1}{(3+r)^2}

Now E_1+E_2=0

\frac{k\times 11.5}{(r+3)^2}\frac{k\times (-1.2)}{r^2}=0

\frac{3+r}{r}=(\frac{11.5}{1.2})^{0.5}

\frac{3+r}{r}=3.095

thus r=1.43\ cm

Thus Electric field is zero at some distance r=1.43 cm right of q_2

3 0
3 years ago
Other questions:
  • 2. In the above figure, what type of cylinder arrangement is shown in the figure above?
    9·1 answer
  • Calculate the availability of a system where the mean time between failures is 900 hours and the mean time to repair is 100 hour
    15·1 answer
  • an adiabatic compressor receives 1.5 meter cube per second of air at 30 degrees celsius and 101 kpa. The discharge pressure is 5
    11·1 answer
  • Help pls I don’t understand the question.
    9·1 answer
  • I NEED HELP ASAP WILL AWARD BRAINLIEST
    8·2 answers
  • For somebody
    12·1 answer
  • A 100-ampere resistor bank is connected to a controller with conductor insulation rated 75°C. The resistors are not used in conj
    8·1 answer
  • Quelles sont les types de carburant utilisés en aviation
    15·1 answer
  • Why do some ladders have a white tip or reflective tape attached to the tip?
    14·1 answer
  • Which - type of service shop is least likely to provide service to all
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!