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Discharge Temperature at High pressure compressor when Cooling ratio is constant Formula

GoDischarge Temperature at High Pressure Compressor given Cooling Ratio Formula

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Discharge Temperature at High Pressure Compressor is the temperature at which refrigerant leaves the compressor. Check FAQs

T 3 = P 1 \cdot (q + (1 - q) \cdot {(\frac{P 2}{P 1})}^{\frac{n c - 1}{n c}})

T₃ - Discharge Temperature at High Pressure Compressor?P₁ - Suction Pressure of Low Pressure Compressor?q - Cooling Ratio?P₂ - Discharge Pressure of Low Pressure Compressor?n_c - Polytropic Index For Compression?

Discharge Temperature at High pressure compressor when Cooling ratio is constant Example

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Here is how the Discharge Temperature at High pressure compressor when Cooling ratio is constant equation looks like with Values.

Here is how the Discharge Temperature at High pressure compressor when Cooling ratio is constant equation looks like with Units.

Here is how the Discharge Temperature at High pressure compressor when Cooling ratio is constant equation looks like.

310.3618 = 0.0024 \cdot (0.9 + (1 - 0.9) \cdot {(\frac{7}{0.0024})}^{\frac{1.2 - 1}{1.2}})

310.3618K = 0.0024Bar \cdot (0.9 + (1 - 0.9) \cdot {(\frac{7Bar}{0.0024Bar})}^{\frac{1.2 - 1}{1.2}})

310.3618 = 0.0024 \cdot (0.9 + (1 - 0.9) \cdot {(\frac{7}{0.0024})}^{\frac{1.2 - 1}{1.2}})

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Discharge Temperature at High pressure compressor when Cooling ratio is constant Solution

Follow our step by step solution on how to calculate Discharge Temperature at High pressure compressor when Cooling ratio is constant?

FIRST Step Consider the formula

T 3 = P 1 \cdot (q + (1 - q) \cdot {(\frac{P 2}{P 1})}^{\frac{n c - 1}{n c}})

Next Step Substitute values of Variables

∴

T 3 = 0.0024Bar \cdot (0.9 + (1 - 0.9) \cdot {(\frac{7Bar}{0.0024Bar})}^{\frac{1.2 - 1}{1.2}})

Next Step Convert Units

∴

T 3 = 243Pa \cdot (0.9 + (1 - 0.9) \cdot {(\frac{700000Pa}{243Pa})}^{\frac{1.2 - 1}{1.2}})

Next Step Prepare to Evaluate

∴

T 3 = 243 \cdot (0.9 + (1 - 0.9) \cdot {(\frac{700000}{243})}^{\frac{1.2 - 1}{1.2}})

Next Step Evaluate

∴

T 3 = 310.361769028767K

LAST Step Rounding Answer

∴

T 3 = 310.3618K

Discharge Temperature at High pressure compressor when Cooling ratio is constant Formula Elements

Variables

Discharge Temperature at High Pressure Compressor

Discharge Temperature at High Pressure Compressor is the temperature at which refrigerant leaves the compressor.

Symbol: T₃

Measurement: TemperatureUnit: K

Note: Value can be positive or negative.

Formulas to find Discharge Temperature at High Pressure Compressor

Suction Pressure of Low Pressure Compressor

Suction Pressure of Low Pressure Compressor is the pressure of the refrigerant at the point where it enters the Low pressure compressor. It is also called Evaporator pressure.

Symbol: P₁

Measurement: PressureUnit: Bar

Note: Value can be positive or negative.

Formulas to find Suction Pressure of Low Pressure Compressor

Cooling Ratio

Cooling Ratio is defined as the ratio of heat abstracted by the cooling system to the heat abstracted to bring the refrigerant to the initial temperature.

Symbol: q

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Cooling Ratio

Discharge Pressure of Low Pressure Compressor

The Discharge pressure of Low pressure compressor is the pressure of the refrigerant at the point where it exits the Low-Pressure compressor. It is also called Pressure at the entry of intercooler.

Symbol: P₂

Measurement: PressureUnit: Bar

Note: Value can be positive or negative.

Formulas to find Discharge Pressure of Low Pressure Compressor

Polytropic Index For Compression

Polytropic Index For Compression is that defined via a polytropic equation of state of the form P∝ρ1+1/n, where P is pressure, ρ is density, and n is the polytropic index.

Symbol: n_c

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Polytropic Index For Compression

Other Formulas to find Discharge Temperature at High Pressure Compressor

Go Discharge Temperature at High Pressure Compressor given Cooling Ratio

T 3 = T 2 - q \cdot (T 2 - T 1)

Other formulas in Minimum Work category

Go Minimum Work required when Temperature at end of Cooling in Intercooler is fixed

W = 2 \cdot (\frac{n c}{n c - 1}) \cdot m \cdot [R] \cdot T 1 \cdot ({(\frac{P 3}{P 1})}^{\frac{n c - 1}{2 \cdot n c}} - 1)

Go Minimum Work required when Cooling Ratio is fixed

W = (\frac{n c}{n c - 1}) \cdot m \cdot [R] \cdot ((T 1 \cdot {(\frac{P 3}{P 1})}^{\frac{n c - 1}{2 \cdot n c}} + T d \cdot {(\frac{P 3}{P 1})}^{\frac{n c - 1}{2 \cdot n c}} - T 1 - T 3))

Go Cooling ratio

q = \frac{T 2 - T 3}{T 2 - T 1}

Go Minimum Work required when Cooling Ratio is fixed and Intercooling is Perfect

W = 2 \cdot (\frac{n c}{n c - 1}) \cdot m \cdot [R] \cdot T r \cdot ({(\frac{P 3}{P 1})}^{\frac{n c - 1}{2 \cdot n c}} - 1)

How to Evaluate Discharge Temperature at High pressure compressor when Cooling ratio is constant?

Discharge Temperature at High pressure compressor when Cooling ratio is constant evaluator uses Discharge Temperature at High Pressure Compressor = Suction Pressure of Low Pressure Compressor*(Cooling Ratio+(1-Cooling Ratio)*(Discharge Pressure of Low Pressure Compressor/Suction Pressure of Low Pressure Compressor)^((Polytropic Index For Compression-1)/Polytropic Index For Compression)) to evaluate the Discharge Temperature at High Pressure Compressor, Discharge Temperature at High pressure compressor when Cooling ratio is constant formula is defined as the temperature at the outlet of a high-pressure compressor when the cooling ratio is constant, which is a critical parameter in determining the performance and efficiency of a compressor in a refrigeration or gas compression system. Discharge Temperature at High Pressure Compressor is denoted by T₃ symbol.

How to evaluate Discharge Temperature at High pressure compressor when Cooling ratio is constant using this online evaluator? To use this online evaluator for Discharge Temperature at High pressure compressor when Cooling ratio is constant, enter Suction Pressure of Low Pressure Compressor (P₁), Cooling Ratio (q), Discharge Pressure of Low Pressure Compressor (P₂) & Polytropic Index For Compression (n_c) and hit the calculate button.

FAQs on Discharge Temperature at High pressure compressor when Cooling ratio is constant

What is the formula to find Discharge Temperature at High pressure compressor when Cooling ratio is constant?

The formula of Discharge Temperature at High pressure compressor when Cooling ratio is constant is expressed as Discharge Temperature at High Pressure Compressor = Suction Pressure of Low Pressure Compressor*(Cooling Ratio+(1-Cooling Ratio)*(Discharge Pressure of Low Pressure Compressor/Suction Pressure of Low Pressure Compressor)^((Polytropic Index For Compression-1)/Polytropic Index For Compression)). Here is an example- 200.0389 = 243*(0.9+(1-0.9)*(700000/243)^((1.2-1)/1.2)).

How to calculate Discharge Temperature at High pressure compressor when Cooling ratio is constant?

With Suction Pressure of Low Pressure Compressor (P₁), Cooling Ratio (q), Discharge Pressure of Low Pressure Compressor (P₂) & Polytropic Index For Compression (n_c) we can find Discharge Temperature at High pressure compressor when Cooling ratio is constant using the formula - Discharge Temperature at High Pressure Compressor = Suction Pressure of Low Pressure Compressor*(Cooling Ratio+(1-Cooling Ratio)*(Discharge Pressure of Low Pressure Compressor/Suction Pressure of Low Pressure Compressor)^((Polytropic Index For Compression-1)/Polytropic Index For Compression)).

What are the other ways to Calculate Discharge Temperature at High Pressure Compressor?

Here are the different ways to Calculate Discharge Temperature at High Pressure Compressor-

Discharge Temperature at High Pressure Compressor=Suction Temperature at High Pressure Compressor-Cooling Ratio*(Suction Temperature at High Pressure Compressor-Suction Temperature at Low Pressure Compressor)

Can the Discharge Temperature at High pressure compressor when Cooling ratio is constant be negative?

Yes, the Discharge Temperature at High pressure compressor when Cooling ratio is constant, measured in Temperature can be negative.

Which unit is used to measure Discharge Temperature at High pressure compressor when Cooling ratio is constant?

Discharge Temperature at High pressure compressor when Cooling ratio is constant is usually measured using the Kelvin[K] for Temperature. Celsius[K], Fahrenheit[K], Rankine[K] are the few other units in which Discharge Temperature at High pressure compressor when Cooling ratio is constant can be measured.

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Discharge Temperature at High pressure compressor when Cooling ratio is constant Formula

​GoDischarge Temperature at High Pressure Compressor given Cooling Ratio Formula

Discharge Temperature at High pressure compressor when Cooling ratio is constant Example

Discharge Temperature at High pressure compressor when Cooling ratio is constant Solution

Discharge Temperature at High pressure compressor when Cooling ratio is constant Formula Elements

Other Formulas to find Discharge Temperature at High Pressure Compressor

Other formulas in Minimum Work category

How to Evaluate Discharge Temperature at High pressure compressor when Cooling ratio is constant?

FAQs on Discharge Temperature at High pressure compressor when Cooling ratio is constant

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GoDischarge Temperature at High Pressure Compressor given Cooling Ratio Formula