Air at a temperature of 27°C flows into a centrifugal compressor running at 20,000 rpm. The following data are given:

Slip factor 0.80

Power input factor 1

Isentropic efficiency 80%

Outer diameter of blade tip 0.5 m

Assuming the absolute velocities of air entering and leaving the compressor are same, find (i) static temperature rise of air passing through the compressor, and (ii) the static pressure ratio.

Question

Air at a temperature of 27°C flows into a centrifugal compressor running at 20,000 rpm. The following data are given:

Slip factor	0.80
Power input factor	1
Isentropic efficiency	80%
Outer diameter of blade tip	0.5 m

Assuming the absolute velocities of air entering and leaving the compressor are same, find (i) static temperature rise of air passing through the compressor, and (ii) the static pressure ratio.

Accepted Answer

Velocity of the blade tip,

[latex] U_{2}=\frac{\pi imes 0.5 imes 20,000}{60} [/latex]

[latex] =523.6 \mathrm{~m} / \mathrm{s} [/latex]

From Eq. (16.5),

[latex] w=\Psi \sigma U_{2}^{2}=c_{p}\left(T_{2 t}-T_{1 t} ight) [/latex] (16.5)

Stagnation temperature rise [latex] \left(T_{2 t}-T_{1 t} ight)=\frac{\psi \sigma U_{2}^{2}}{c_{p}} [/latex]

[latex] =\frac{0.80 imes(523.6)^{2}}{1005}=218.23^{\circ} \mathrm{C} [/latex]

([latex] c_{p} [/latex] of air has been taken as 1005 J/kg K)

Since the absolute velocities at the inlet and the outlet of the stage are the same, the rise in stagnation temperature equals to that in static temperature.

The static pressure ratio can be written as

[latex] \frac{p_{2}}{p_{1}}=\left(\frac{T_{2}^{\prime}}{T_{1}} ight)^{\frac{\gamma}{\gamma-1}} [/latex]

[latex] =\left[1+\frac{\eta_{C}\left(T_{2}-T_{1} ight)}{T_{1}} ight]^{\frac{\gamma}{\gamma-1}} [/latex]

[latex] =\left[1+\frac{0.8 imes 218.23}{300} ight]^{\frac{1.4}{0.4}} [/latex]

=4.98

Question 16.4: Air at a temperature of 27°C flows into a centrifugal compre...

Related Answered Questions

A centrifugal fan running at 1500 rpm has inner and outer diameter of the impeller as 0.2 m and 0.24 m. The absolute and relative velocities of air at entry are 21 m/s and 20 m/s respectively and those at exit are 25 m/s and 18 m/s respectively. The flow rate is 0.6 kg/s and the motor efficiency ...

Verified Answer:

The preliminary design of an axial flow compressor is to be based upon a simplified consideration of the mean diameter conditions. Suppose that the characteristics of a repeating stage of such a design are as follows: Stagnation temperature rise (ΔTst) 30 K Degree of reaction (Λ) 0.6 Flow ...

Verified Answer:

The conditions of air at the entry of an axial flow compressor stage are p1 = 100kN/m^2 and Tl = 300 K. The air angles are β1 = 51º, β2 = 10º, a1 = a 3 = 8º. The mean diameter and peripheral speed are 0.5 m and 150 m/s respectively. Mass flow rate through the stage is 30 kg/s; the work done ...

Verified Answer:

At the mean diameter, U = 200 m/s, V f = 180 m/s, β1 = 43.9° and β2 = 13.5°. The factor λ = 0.86 and ηs = 0.85 and inlet temperature T1t is 288 K. Calculate the pressure ratio. ...

Verified Answer:

A centrifugal compressor has an impeller tip speed of 360 m/s. Determine (i) the absolute Mach number of flow leaving the radial vanes of the impeller and (ii) the mass flow rate. The following data are given: Impeller Tip speed 360 m/s Radial component of flow velocity at impeller exit 30 m/s ...

Verified Answer:

Determine the pressure ratio developed and the specific work input to drive a centrifugal air compressor of an impeller diameter of 0.5 m and running at 7000 rpm. Assume zero whirl at the entry and T1t = 290 K. The slip factor and power input factor to be unity, the process of compression is ...

Verified Answer:

Air at a stagnation temperature of 27º C enters the impeller of a centrifugal compressor in the axial direction. The rotor which has 15 radial vanes, rotates at 20000 rpm. The stagnation pressure ratio between the diffuser outlet and the impeller inlet is 4 and the isentropic efficiency is 85%. ...

Verified Answer: