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Articles by Dr Pankaj Dumka
Page 2 of 2
Solving the First Law of Thermodynamics using Python
The first law of thermodynamics is related to energy conservation, i.e., if energy in form disappears then the energy will in appear in some other form. In thermodynamics majorly we are concerned about heat, work and internal energy. Heat and work are the form of energy which are also called as "energy in transit", hence they are path functions. They cannot be stored by a system, whereas internal energy is the property of the system which can be stored by system. For a closed system, the first law is written as − $$\mathrm{\Sigma Q=\Sigma W}$$ But this is only valid ...
Read MoreModelling the Rankine Cycle in Python
Rankine cycle is the heart of any thermal power plant. A basic Rankine cycle has four processes, viz. reversible adiabatic work interactions in turbine and pump and isobaric heat interactions in boiler and condenser. A schematic of a thermal power plant is shown in the figure given below. To increase the efficiency of a Rankine cycle Regeneration has been used i.e. bleeding steam to turbine and mixing it with feed water in feed water heater. Different processes in the cycle have to be modelled with the help of data from stream tables. Therefore, it becomes very essential to have ...
Read MoreModelling the Secant Method in Python
Secant method is one of the powerful methods to know the x-intercept (zeros) of a polynomial or any transcendental function. In this method, first we select (basically guess) the interval in which we expect the root ($\mathrm{𝑥_{1}}$, $\mathrm{𝑥_{2}}$). Then we draw a secant line to join the points on the function (A, B) corresponding to the guessed values as shown in the figure below. The secant line intersects the x-axis at the point $\mathrm{𝑥_{3}}$, as $\mathrm{𝑥_{3}}$ and $\mathrm{𝑥_{2}}$ are not close (i.e., their absolute difference is finite) we find the point corresponding to 𝑥3 on the curve i.e., C. ...
Read MoreModelling the Regula Falsi Method in Python
In this tutorial, I will show you how to find the roots of an equation with the help of Regula Falsi which is also called as the "False Position Method". Let us consider the figure shown below. First we have searched for two 𝑥 values $\mathrm{x_{1}}$ and $\mathrm{x_{2}}$ at which the value of function ($\mathrm{y_{1}} $and $\mathrm{y_{2}}$) are different, means the points should be such that the products of these two should be negative (i.e. they should lie on the opposite sides of the X-axis). As these are not the exact point i.e. the points at which root exist, ...
Read MoreModelling the Newton Raphson Method in Python
In this tutorial, I will show you how to evaluate the roots of a polynomial or transcendental equation with the help of a numerical method known as the Newton Raphson method. This is an iterative method in which we start with a initial guess (of independent variable) and then evaluate the new value of 𝑥 based on the guess. And the process goes on till the convergence is achieved. The method is explained with the help of a diagram as shown below. Based on $x_{g}$ the value of function $(f^{'} \left ( x_{g} \right ))$ is evaluated. Then a ...
Read MoreModelling the Projectile Motion using Python
Let us first understand some basic concepts and equations based on which the projectile motion can be modelled. The figure shown below explains some basic terminologies of projectile motion. Here, "u" is the velocity with which the projectile is being projected. 𝛼 is the angle of projection of the projectile. The path taken up by the projectile during its flight. Range is the maximum horizontal distance travelled by the projectile. $\mathrm{h_{max}}$ is the maximum height attained by the projectile. Moreover, the time taken up by the projectile to travel the range is called as time of flight. The projectile ...
Read MoreModelling the Carnot Cycle in Python
Carnot cycle is the most fundamental gas power cycle. This is the cycle which acts as a benchmark for any engine cycle. Each and every engine cycle efficiency is checked against the Carnot Cycle. If an inventor develops a new engine cycle, then it has to be validated against the benchmark, i.e., the Carnot Cycle. All thermodynamic cycle has an upper limit established by the Carnot cycle. It comprises of two reversible adiabatic processes and two isothermal processes, in total four processes. Isothermal processes involve the addition and rejection of heat, whereas reversible adiabatic processes involve work interactions. A ...
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