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

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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.
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

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.)
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.)

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.
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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