Flight Mechanics Archives - ToDo Calculator

isentropic area mach number relation

Pawan Indalkar — Thu, 09 Jan 2025 16:25:46 +0000

Problem Statement:

A perfect gas flows isentropically through a nozzle. If the ratio of the nozzle exit to the throat is 3.0, and the exit Mach number is also 3.0, find the specific heats ratio of the gas.

Equation:01

Isentropic Relations:

Equation 2:Mach Number

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.)

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pressure ratio, mach number, velocity,density,speed of sound,mach number

Pawan Indalkar — Wed, 01 Jan 2025 16:15:18 +0000

Problem statement: Compressed air at 40 ∘C and 145 kPa from a large tank is discharged to ambient atmosphere at 101 kPa, through a convergent nozzle of 10 cm2 exit area, Calculate the mass flow rate through
the nozzle when the ambient atmosphere is at (a) 101 kPa, (b) 50 kPa, and (c) 30 kPa.

Equation :01 pressure ratio

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.

Equation 2: Mach Number

Equation 3:speed of sound

More simply, the speed of sound is how fast vibrations travel. At 20 °C (68 °F), the speed of sound in air is about 343 m/s (1,125 ft/s; 1,235 km/h; 767 mph; 667 kn), or 1 km in 2.91 s or one mile in 4.69 s. It depends strongly on temperature as well as the medium through which a sound wave is propagating.

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pressure ratio, mach number, velocity,density,speed of sound,mach number

Pawan Indalkar — Fri, 13 Dec 2024 16:36:53 +0000

Probelm Statement:

Compressed air at 40 ∘C and 145 kPa from a large tank is discharged to ambient atmosphere at 101 kPa, through a convergent nozzle of 10 cm2 exit area,Calculate the mass flow rate through
the nozzle when the ambient atmosphere is at (a) 101 kPa, (b) 50 kPa, and (c) 30 kPa.

Equations Used:

Equation 1: Pressure Ratio

Pressure is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure is the pressure relative to the ambient pressure. Various units are used to express pressure.

Equation 2:Mach Number

Equation 3:Velocity

the speed at which something moves in a particular direction

Equation 4: Density

Mass Per Unit Volume

Equation 4:Speed of Sound

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Energy Equation , Mass flow Rate

Pawan Indalkar — Fri, 22 Nov 2024 17:24:29 +0000

Problem statement:A flow at 60 m s−1 enters a nozzle kept horizontal. The specific enthalpy at the nozzle inlet and exit is 3025 and 2790 kJ kg−1, respectively,Neglecting the heat loss from the nozzle, calculate
(a) the flow velocity at the nozzle exit, (b) the mass flow rate through the nozzle, if the inlet area
is 0.1 m2 and the specific volume at inlet is 0.19 m3 kg−1, and (c) the exit area of the nozzle when
the specific volume at the exit is 0.5 m3 kg−1.

Equation 1:

The equation developed by Albert Einstein, which is usually given as E = mc², showing that, when the energy of a body changes by an amount E (no matter what form the energy takes), the mass (m) of the body will change by an amount equal to E/c².

Energy = Power x Time.

Equation 2:

Mass flow rate can be calculated by multiplying the volume flow rate by the mass density of the fluid, ρ. The volume flow rate is calculated by multiplying the flow velocity of the mass elements, v, by the cross-sectional vector area, A.

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Mass flow rate, mach number, pressure, Isentropic Relation

Pawan Indalkar — Wed, 20 Nov 2024 17:33:05 +0000

problem statement:

Helium gas from a storage tank at 1000 kPa and 310 K is flowing out through a convergent nozzle of exit area 3 cm2 to another tank.When the mass flow rate is 0.15 kg s−1, determine the
pressure in the second tank.

Solution Equations used:

The mass flow rate formula is m=ρVA, where ρ is the density of fluid, V is the velocity of the liquid, and A is the area of cross-section.

2: Mach Number:

3:Pressure:

4: Isentropic Relations:

Isentropic relations are important for analyzing the flow of compressible fluids, like gases, especially when there is no heat transfer or friction. They help predict how pressure, temperature, and density change in a flowing fluid without external heat sources or viscous effects.

The term “isentropic” comes from the Greek words isos, meaning equal, and entropia, meaning entropy. Entropy is a measure of disorder or randomness in a closed system.

In real-world applications, the isentropic process is an approximation because it’s not possible to completely isolate a system. However, the concept is useful for simplifying the analysis and calculation of various thermodynamic processes.

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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,

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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).

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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Coefficient Of Lift For Max Glide Endurance Calculator

Ravula Nikhil Reddy — Tue, 26 Mar 2024 04:15:30 +0000

The Coefficient of Lift for Max Glide Endurance is a parameter that signifies the lift efficiency required for achieving the longest possible duration of unpowered flight. It represents the ratio of the lift force generated by the aircraft’s wings to the dynamic pressure of the surrounding air and the wing’s area. In the context of maximizing glide endurance, this coefficient indicates the optimal lift-to-drag ratio attained by adjusting the aircraft’s angle of attack. By operating at the angle of attack corresponding to the maximum lift coefficient, aircraft can sustain flight for extended periods without engine power, crucial for applications like gliders or endurance UAVs. The formula to calculate Coefficient of lift for Max Glide Endurance as follows:

Where:

C_L is the Coefficient of Lift,
C_D0 is the Zero Lift Drag Coefficient,
K is the Constant, (K=1/(pi*e*AR)).

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Thrust Available For Level And Unaccelerated Flight Calculator

Ravula Nikhil Reddy — Tue, 19 Mar 2024 08:52:47 +0000

Thrust is the force generated by a propulsion system, typically provided by engines or jet propulsion, to propel an object forward. If excess power increases relative to thrust, the aircraft gains more surplus power for improved climbing and acceleration; a decrease in excess power compared to thrust can hinder these performance aspects. The formula to calculate the thrust is as follows:

Where:

CD is the Drag Coefficient,
CL is the Lift Coefficient,
W is the aircraft weight in N.

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Flight Path Angle given By Glide Range Calculator

Ravula Nikhil Reddy — Tue, 19 Mar 2024 06:57:04 +0000

The Flight Path Angle (FPA) is the angle between an aircraft’s velocity vector and the horizontal plane. It represents the trajectory of the aircraft in three-dimensional space. Positive Flight path angle indicates a climb, negative FPA denotes a descent, and zero Flight path angle corresponds to level flight. FPA is a crucial parameter for understanding an aircraft’s vertical movement during flight. The flight path angle formula is derived from the forces acting on gliding flight. The formula to calculate flight path angle is as follows:

Where:

R is the Glide Range in m,
H is the Altitude at the start of the glide in m.

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