Reynolds Number Formula & Kinetic Energy Formula & Fahrenheit to Celsius Formula.

Reynolds Number Formula

                                                                                                                                                                                    Source:Pinterest.com

R = inertialforceviscousforce

R = refers to the Reynolds Number that is unitless

Solved Examples on Reynolds Number Formula

Q. Let’s assume that we are doing a research project on water flowing through pipes. We also want to compare the diameters of the two pipes exhibiting laminar flow in which water flows smoothly in a conventional fashion.

In addition, pipes that show turbulent flow where water flow chaotically, that make forecasts involving its flow difficult. Furthermore, it can cause vibration that can cause premature wear and tear in the flow system causing its failure.

In our research project, we want Reynolds number of 2200 for the water flowing through the two separate pipes. In this, the first pipe has a diameter of 2.75 cm (0.0275 m). Also, the density of water is 1,000 Kg/m3. Above all, the viscosity of water is 0.0013 kg/(m⋅ s). Calculate what velocity the water has to pass through the pipe to fit these parameters?

Solution:

2000 = 1000(kgm3)ν(0.0275m)0.00133Pa⋅s

ν≈0.01ms

Now, we have to use different pipe of different diameters with the same setup, also calculate the velocity of the water that should pass through it. Moreover, we will put a dye in flowing water when it is flowing through the pipe at a calculated velocity.

Also, if the dye water comes out displaying laminar flow then we just show how dynamic similitude works. Now, let’s do the final calculation to determine the velocity of the water that should flow through a smaller pipe.

2000 = 1000(kgm3)ν(0.005m)0.00133Pa⋅s

ν≈0.05ms

After the calculation, we come to the calculation that the water in the smaller pipe flows faster than the water in a bigger pipe. Also, even after the water of the smaller pipe flows faster it still shows laminar fashion because the Reynolds number is the same as in the previous scenario.

Kinetic Energy Formula

For the Kinetic formula, Ek, is certainly the energy of a mass, m, motion, of course, is v2.

Ek = 1/2 mv2

Ek = Kinetic energy

m = mass of the body

v = velocity of the body

Kinetic Energy Formula Derivation

Let us consider the example of an object of m which is at a state of rest on a table.

A force F acts on the object which moves it through a distance S.

The work done=F x S

W=Fnet x S——-(1)

Consider the work done on the object which results in a change in velocity from u to V. Furthermore, one must let “a” be the acceleration.

Considering the third equation of motion:

V²-u²=2as

s=V²-u²/2a———-(2)

Applying Newton’s Second law:

F=ma——(3)

From equation (1), (2) and (3)

W=ma*(V²-u²/2a)\=(1/2)m(V²-u²)

As the object in a state of rest, u=0

W=(1/2)mV²

Furthermore, the kinetic energy of a body moving with a certain velocity is equal to work done on the object. This work is for the purpose of acquiring that velocity from the estate of rest.

Therefore, Kinetic energy =1/2 mV²

Solved Examples on Kinetic Energy Formula

Q1 The mass of a bicycle is 10 kg, and it moves at a constant velocity of 10 km/h. Find out the kinetic energy of this bicycle?

A1 Here the mass is “m’ and the velocity is “v”. Also, m = 10 kg and v = 10 km/h. Now, one must apply the kinetic energy equation:

Ek = 1/2 mv2

Ek = 1/2 (10 kg) (10km/h)

Ek = 50 Joules

Hence, the kinetic energy, in this case, is 50 Joules.

Q2 The kinetic energy of the car is 300,000 Joules and its velocity is 30 m/s. Find out the mass of the vehicle?

A2 The kinetic energy of the car in motion is certainly Ek = 300,000 J = 30,000 kg m2/s2. Moreover, the velocity of the car which is v = 30 m/s

Ek = 1/2 mv2

Ek/0.5v2 = m

m = (300,000 kg m2/s2)/[0.5(30m/s)2]

m = (300,000 kg m2/s2/[(0.5)(900)m2/s2]

m = (300,000 kg m2/s2/450 m2/s2

m = 666.666 kg

Hence, the mass of the vehicle = 666.666 kg

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