Any help is appreciated.

Consider a vortex filament of strength in the shape of a closed circular loop of radius R. Obtain an expression for the velocity

zysi [14]

Answer:

v = T/(2R)

Explanation:

Given

R = radius

T = strength

From Biot - Savart Law

dv = (T/4π)* (dl x r)/r³

Velocity induced at center

v = ∫ (T/4π)* (dl x r)/r³

⇒ v = ∫ (T/4π)* (dl x R)/R³ (k) k: unit vector perpendicular to plane of loop

⇒ v = (T/4π)(1/R²) ∫ dl

If l ∈ (0, 2πR)

⇒ v = (T/4π)(1/R²)(2πR) (k) ⇒ v = T/(2R) (k)

3 0

3 years ago

A metallic material with yield stress of 140 MPa and cross section of 300 mm x 100 mm, is subjected to a tensile force of 8.00 M

Readme [11.4K]

Answer:Yes,266.66 MPa

Explanation:

Given

Yield stress of material =140 MPa

Cross-section of $300\times 100 mm^2$

Force(F)=8 MN

Therefore stress due to this Force( $\sigma$ )

$\sigma =\frac{F}{A}=\frac{8\times 10^6}{300\times 100\times 10^{-6}}$

$\sigma =266.66 \times 10^{6} Pa$

$\sigma =266.66 MPa$

Since induced stress is greater than Yield stress therefore Plastic deformation occurs

8 0

2 years ago

A room has a width of 14.1 feet, a length of 15.5 feet, and a ceiling height of 12.0 ft. The average flow rate for this room's a

prohojiy [21]

Answer:

Your question lacks the time required hence i will calculate the Average flow rate using a general concept and an assumed time value of 25 seconds

ANSWER : 104.904 ft^3/sec

Explanation:

General concept : Average flow rate is the volume of fluid per unit time through an area

Hence the average flow rate of the air conditioning unit of this room

Volume of the room / time taken for the air to cycle the room = v / t

assuming the time taken = 25 seconds

volume of room = width * length * height

= 14.1 * 15.5 * 12 = 2622.6 ft^3

Average flow rate = V/ t

= 2622.6 / 25 = 104.904 ft^3/sec

8 0

2 years ago

1. What is the maximum value of the linear density in a crystalline solid (linear density defined as the fraction of the line le

insens350 [35]

Number three number three number three I’m not 100% sure though

4 0

2 years ago

In the circuit given below, R1 = 17 kΩ, R2 = 74 kΩ, and R3 = 5 MΩ. Calculate the gain 1formula58.mml when the switch is in posit

Elenna [48]

Answer:a

a) Vo/Vi = - 3.4

b) Vo/Vi = - 14.8

c) Vo/Vi = - 1000

Explanation:

a)

R1 = 17kΩ

for ideal op-amp

Va≈Vb=0 so Va=0

(Va - Vi)/5kΩ + (Va -Vo)/17kΩ = 0

sin we know Va≈Vb=0

so

-Vi/5kΩ + -Vo/17kΩ = 0

Vo/Vi = - 17k/5k

Vo/Vi = -3.4

║Vo/Vi ║ = 3.4 ( negative sign phase inversion)

b)

R2 = 74kΩ

for ideal op-amp

Va≈Vb=0 so Va=0

so

(Va-Vi)/5kΩ + (Va-Vo)74kΩ = 0

-Vi/5kΩ + -Vo/74kΩ = 0

Vo/Vi = - 74kΩ/5kΩ

Vo/Vi = - 14.8

║Vo/Vi ║ = 14.8 ( negative sign phase inversion)

c)

Also for ideal op-amp

Va≈Vb=0 so Va=0

Now for position 3 we apply nodal analysis we got at position 1

(Va - Vi)/5kΩ + (Va - Vo)/5000kΩ = 0 ( 5MΩ = 5000kΩ )

so

-Vi/5kΩ + -Vo/5000kΩ = 0

Vo/Vi = - 5000kΩ/5kΩ

Vo/Vi = - 1000

║Vo/Vi ║ = 1000 ( negative sign phase inversion)

3 0

2 years ago