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arsen [322]
3 years ago
12

Liquid flows with a free surface around a bend. The liquid is inviscid and incompressible, and the flow is steady and irrotation

al. The velocity varied with the radius across the flow as V = 1/r m/s where r is in meters. Find the difference in depth of the liquid from the inside to the outside radius. The inside radius of the bend is 1 m and the outside radius is 3 m.
Engineering
1 answer:
lions [1.4K]3 years ago
3 0

Answer:

9 cm

Explanation:

The liquid on the bend will be affected by two accelerations: gravity and centripetal force.

Gravity will be of 9.81 m/s^2 pointing down at all points.

The centripetal acceleration will be of

ac = v^2/r

Pointing to the center of the bend (perpendicular to gravity).

The velocity will depend on the radius

v = (1 m^2/s) / r

Replacing:

ac = (1/r)^2 / r

ac = (1 m^4/s^2) / r^3

If we set up a cylindrical reference system with origin at the center of the bend, the total acceleration will be

a = (-1/r^3 * i - 9.81 * j)

The surface of the liquid will be an equipotential surface, this means all points on the surface have the same potential energy.

The potential energy of the gravity field is:

pg = g * h

The potential energy of the centripetal force is:

pc = ac * r

Then the potential field is:

p = -1/r^2 * - 9.81*h

Points on the surface at r = 1 m and r = 3 m have the same potential.

-1/1^2 * - 9.81*h1 = -1/3^2 * - 9.81*h2

-1 - 9.81*h1 = -1/9 - 9.81*h2

-1 + 1/9 = 9.81 * (h1 - h2)

h1 - h2 = (-8/9) / 9.81

h2 - h1 = 0.09 m

The outer part will be 9 cm higher than the inner part.

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Dmitrij [34]

As much as the human and physical capital in economy increases, there is a decrease in the marginal gain in economic growth that will diminish.

<u>Explanation:</u>

Low-income countries might have an advantage achieving greater worker productivity and economic growth in the future as their economic growth is faster than the high - income countries.

As much as the human and physical capital in economy increases, there is a decrease in the marginal gain in economic growth that will diminish. And this is called, the laws of diminishing returns.

Secondly, low - income countries find it easier in developing technologies than the high - income technologies especially countries like India and China.

High - income countries put effort in inventing new technologies, whereas low - income countries just improve and improvise their technology.

3 0
3 years ago
The specific gravity of a substance that has mass of 10 kg and occupies a volume of 0.02 m^3 is a) 0.5 b) 1.5 c) 2.5 d) 3.5 e) n
zhuklara [117]

Answer:

Specific gravity is 0.5 so option (a) is correct option

Explanation:

We have given mass of substance m =10 kg

Volume V=0.02m^3

Density of substance is given by Density\ d=\frac{mass}{volume}=\frac{10}{0.02}=500kg/m^3

Specific gravity is given by specific\ gravity=\frac{density\ of\ substance}{density\ f\ water}=\frac{500}{1000}=0.5

So option (a) is correct option

5 0
3 years ago
Design a PI controller to improve the steady-state error. The system should operate with a damping ratio of 0.8. Compute the ove
blondinia [14]

Answer:

The MATLAB Code for this PI Controller will be:

Kp = 350;

Ki = 300;

Kd = 50;

C = pid(Kp,Ki,Kd)

T = feedback(C*P,1);

t = 0:0.01:2;

step(T,t)

Explanation:

When you are designing a PID controller for a given system, follow the steps shown below to obtain a desired response.

Obtain an open-loop response and determine what needs to be improved

Add a proportional control to improve the rise time

Add a derivative control to reduce the overshoot

Add an integral control to reduce the steady-state error

Adjust each of the gains $K_p$, $K_i$, and $K_d$ until you obtain a desired overall response.

The further explanation is attached in the Word File.

Download docx
5 0
3 years ago
What is the activation energy (Q) for a vacancy formation if 10 moles of a metal have 2.3 X 10^13 vacancies at 425°C?
Yakvenalex [24]

Answer:

Activation\ Energy=2.5\times 10^{-19}\ J

Explanation:

Using the expression shown below as:

N_v=N\times e^{-\frac {Q_v}{k\times T}

Where,

N_v is the number of vacancies

N is the number of defective sites

k is Boltzmann's constant = 1.38\times 10^{-23}\ J/K

{Q_v} is the activation energy

T is the temperature

Given that:

N_v=2.3\times 10^{13}

N = 10 moles

1 mole = 6.023\times 10^{23}

So,

N = 10\times 6.023\times 10^{23}=6.023\times 10^{24}

Temperature = 425°C

The conversion of T( °C) to T(K) is shown below:

T(K) = T( °C) + 273.15  

So,  

T = (425 + 273.15) K = 698.15 K  

T = 698.15 K

Applying the values as:

2.3\times 10^{13}=6.023\times 10^{24}\times e^{-\frac {Q_v}{1.38\times 10^{-23}\times 698.15}

ln[\frac {2.3}{6.023}\times 10^{-11}]=-\frac {Q_v}{1.38\times 10^{-23}\times 698.15}

Q_v=2.5\times 10^{-19}\ J

4 0
3 years ago
Name two common fuel gases that can be used for oxyfuel cutting
zlopas [31]
Hi

Acetylene and propane

I hope this help you!
8 0
1 year ago
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