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Entropy , Isentropic , Power Required Equations

Pawan Indalkar — Fri, 15 Nov 2024 08:44:34 +0000

Entropy can be calculated using the formula ΔS=∫(dq/T), where ΔS is the change in entropy, dq is the infinitesimal amount of heat transferred, and T is the temperature at which the heat transfer occurs.

Isentropic relations are thermodynamic relationships that describe how a fluid behaves during an isentropic process. An isentropic process is a reversible adiabatic process where entropy remains constant.
Isentropic relations are important for analyzing the flow of compressible fluids, such as gases, in scenarios without heat transfer or friction. They help predict how pressure, temperature, and density change in a flowing fluid.
Here are some key points about isentropic relations:
Definition
The term “isentropic” comes from the Greek words isos meaning equal and entropia meaning entropy.
Idealization
An isentropic process is an idealization of an actual method. In real-world applications, total isolation of a system is not possible, so the isentropic process is an approximation.
Examples
Pumps, turbines, nozzles, gas compressors, and diffusers are examples of devices that can be analyzed using isentropic relations.
Mach number
The Mach number plays an important role in isentropic relations. If the Mach number of the flow is determined, all the other flow relations can be determined.The equation for power isP=W/tcap P equals cap W / t
𝑃=𝑊/𝑡
, where:
Pcap P
𝑃
:Power, measured in watts (W)
Wcap W
𝑊
:Work done
tt
𝑡
: Time taken Calculating the Amount of Power Required for an Object to Maintain …
2 Mar 2022 — Power:It is defined as the rate of work done by an object within a specific time interval. The equation for power is as …
Study.com
Power formula – Equations with Related Examples – BYJU’S
P = E t. P = W t. or, Where, The Energy Consumed to do work = E. Work done = W. Time taken= t. In any electrical circuit, the powe…
BYJU’S
Here are some other equations for power:
P=Fd/tcap P equals cap F d / t
𝑃=𝐹𝑑/𝑡
This equation can be used when the force and distance are in the same direction. Power in Physics | Definition, Equation & Examples – Study.com
What is the Equation for Power? * P = W / t. * W = F d. Assuming that the force and distance are in the same direction. Substitut…
Study.com
P=Fvcap P equals cap F v
𝑃=𝐹𝑣
This is known as the force-velocity equation. Power in Physics | Definition, Equation & Examples – Study.com
What is the Equation for Power? * P = W / t. * W = F d. Assuming that the force and distance are in the same direction. Substitut…
Study.com
P=V×Icap P equals cap V cross cap I
𝑃=𝑉×𝐼
This equation is used to calculate power in an electrical circuit in terms of voltage and current. Power formula – Equations with Related Examples – BYJU’S
P = E t. P = W t. or, Where, The Energy Consumed to do work = E. Work done = W. Time taken= t. In any electrical circuit, the powe…
BYJU’S
P=I2Rcap P equals cap I squared cap R
𝑃=𝐼2𝑅
This equation is used to calculate power in an electrical circuit in terms of current and resistance. Power formula – Equations with Related Examples – BYJU’S
P = E t. P = W t. or, Where, The Energy Consumed to do work = E. Work done = W. Time taken= t. In any electrical circuit, the powe…
BYJU’S
P=V2/Rcap P equals cap V squared / cap R
𝑃=𝑉2/𝑅
This equation is used to calculate power in an electrical circuit in terms of voltage and resistance. Power formula – Equations with Related Examples – BYJU’S
P = E t. P = W t. or, Where, The Energy Consumed to do work = E. Work done = W. Time taken= t. In any electrical circuit, the powe…
BYJU’S
Power is the rate at which energy is transferred or converted, or the rate at which work is done.In the metric system, the unit of power is the watt, which is equal to one joule per second.In the English system, the unit of power is the horsepower (hp), which is equal to 550 foot-pounds per second.

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speed of sound, mach number, isentropic relations

Pawan Indalkar — Wed, 13 Nov 2024 12:42:49 +0000

speed o sound formula,

[contact-form]

The speed of sound (a) is equal to the square root of the (g) times the gas constant (R) times the absolute temperature (T). The derivation of this equation is given on a separate page. Notice that the temperature must be specified on an absolute scale (Kelvin or Rankine).

Mach number is calculated by finding the ratio of speed of an object to the speed of sound in the surrounding medium. Mach number is unitless (dimensionless quantity). The formula for calculating Mach number is M = v/c , where M is Mach number, v is the velocity of object (in meters per second, feet per second, etc.)

Isentropic relations are thermodynamic relationships that describe how a fluid behaves during an isentropic process. An isentropic process is a reversible adiabatic process where entropy remains constant. This means that no heat is added to the flow, and no energy is lost due to friction or dissipative effects.
Isentropic relations are important for analyzing the flow of compressible fluids, like gases, especially when there is no heat transfer or friction. They can help predict how pressure, temperature, and density change in a flowing fluid.
Isentropic relations are used in many fields of science and engineering, including:
Fluid dynamics
Isentropic relations are used to model fluid compressibility and are an underlying assumption in aerodynamics.
Energy engineering
Isentropic relations are used to evaluate the isentropic work of gas compression and expansion systems. They are also fundamental to turbo-machinery design.

calculator developed by- Pawan Indalkar

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Gust Effect on Structures Calculator

GULSHAN SHAFI — Sun, 10 Mar 2024 13:06:25 +0000

Gust effect is an Analyzing wind-induced loads for structural safety assessment.The formula is given by:

Where:

$F_{gust}$ is the wind-induced force due to the gust,
$ρ$ is the air density,
$V_{gust}$ is the gust wind speed,
$C_{d}$ is the drag coefficient,
$A$ is the reference area (e.g., the projected area of the structure perpendicular to the wind direction).

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Base Isolation Techniques For Seismic Protection

GULSHAN SHAFI — Sun, 10 Mar 2024 12:57:52 +0000

Base isolation is a Shield structures from earthquakes, enhancing safety.The formula is given by:

Where:

$a_{base}$ is the acceleration response at the base of the isolated structure,
$a_{ground}$ is the ground acceleration input.

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Soil Dynamics And Foundation Vibrations

GULSHAN SHAFI — Sun, 10 Mar 2024 12:41:47 +0000

Critical for stable structures, soil dynamics, foundation vibrations analysis.The formula is given by:

Where:

$F (ω)$ is the Fourier transform of the applied dynamic load,
$U (ω)$ is the Fourier transform of the resulting foundation displacement,
$ω$ is the angular frequency.

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Earthquake Response Spectrum Analysis Calculator

GULSHAN SHAFI — Sun, 10 Mar 2024 12:34:36 +0000

Analyze seismic response for structural design, ensuring safety and resilience.The formula is given by:

Where:

$S_{a} (T)$ is the spectral acceleration at a given period $T$ ,
$S_{d} (T)$ is the design response spectrum at period $T$ ,
$_{A g}$ is the ground acceleration.

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Modal Damping Ratios Determination Calculator

GULSHAN SHAFI — Sun, 10 Mar 2024 12:22:11 +0000

Calculate modal damping ratios for understanding structural vibration behavior.The formula is given by:

Where:

$Δ f$ is the width of the frequency response curve at the -3 dB (half-power) points,
$f_{n}$ is the natural frequency of the mode.

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Forced vibration analysis of structures Calculator

GULSHAN SHAFI — Sun, 10 Mar 2024 12:05:22 +0000

Structure response to external forces studied for dynamic behavior understanding.The formula is given by:

Where:

$M$ is the mass matrix of the structure,
$C$ is the damping matrix,
$K$ is the stiffness matrix,
$u (t)$ is the vector of displacements of the structure at time $t$ ,
$u ¨ (t)$ is the acceleration vector of the structure at time $t$ ,
$u ˙ (t)$ is the velocity vector of the structure at time $t$ ,
$F (t)$ is the vector of external forces or excitations applied to the structure at time $t$ .

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Craig-Bampton Method Calculator

GULSHAN SHAFI — Sun, 10 Mar 2024 11:30:53 +0000

Craig-Bampton method is an Efficient structural dynamics analysis for complex systems.The formula is given by:

Where:

$M_{c}$ and $K_{c}$ are the condensed mass and stiffness matrices of the free component region,
$u ¨_{c}$ and $u_{c}$ are the acceleration and displacement vectors of the boundary degrees of freedom of the free component region,
$F_{c}$ is the external force vector applied to the boundary degrees of freedom.

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R-curve Calculator

GULSHAN SHAFI — Sun, 10 Mar 2024 10:52:55 +0000

Fracture toughness as crack extends, vital for structural analysis.The formula is given by:

Where:

$K_{Ic} (a)$ is the fracture toughness at a given crack length $a$ ,
$K_{Ic} (0)$ is the initial fracture toughness (typically at $a = 0$ ),
$R (a)$ is the increment in fracture toughness as the crack grows.

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