# STEAM NOZZLES CLASS NOTES FOR MECHANICAL ENGNEERING

**STEAM NOZZLES CLASS NOTES FOR**

** MECHANICAL ENGINEERING**

### Turbines and steam engines use

### steam. Turbines produce

### electricity in thermal power plants.

### Turbines use nozzles to produce a high

### velocity jet. This jet runs the steam turbine.

**NOZZLES**

**A nozzle is a passage of variable cross section. A nozzle produces high velocity jet. It converts**

** (i) Pressure energy into kinetic energy**

** (ii) Enthalpy into kinetic energy**

** (iii) Solar energy into electrical energy**

**These jets may be **

**(a) Sub-sonic**

**(b) Sonic **

**(c) Super-sonic**

**These jets are used to produce thrust and hence power.**

**TYPES OF NOZZLES**

**Convergent Nozzles**

**Area reduces from inlet to outlet. Throat has the minimum area at the exit of the convergent portion. Angle of convergence is up to 30**^{0.} Length of convergence is less. These nozzles produce subsonic or sonic jets. At the most, there is sonic veloc**ity at the throat.** Only convergent nozzles are used as spray nozzles.

**Divergent Nozzles———area increases from inlet to outlet—-Rarely used as nozzles. These are used as diffusers—to increase pressure by reducing the velocity.**

**Convergent-divergent nozzles (C-D nozzles)**

^{0.}Length of convergence is less. These nozzles produce subsonic or sonic jets. At the most, there is sonic veloc

**ity at the throat.**

**It is a combination of convergent and divergent portion. Maximum angle of divergence is 12**^{0}. Smaller angle of divergence is to avoid SEPARATION OF FLOW AND EDDY FORMATION. Hence length of divergence is much more than the convergent length. THESE NOZZLES ARE IN MAXIMUM IN USE to get super-sonic jets. Therefore only convergent -divergent nozzles are used in steam turbines to produce power.

^{0}. Smaller angle of divergence is to avoid SEPARATION OF FLOW AND EDDY FORMATION. Hence length of divergence is much more than the convergent length. THESE NOZZLES ARE IN MAXIMUM IN USE to get super-sonic jets.

**PRACTICAL APPLICATIONS OF NOZZLES**

**The high velocity jets are used to run**

** (i) Steam turbines**

** (ii) Gas Turbines**

** (iii) Rockets, jets produce required thrust for supersonic flight**

** (iv) Spray nozzles used in industry**

**EFFICIENCY OF A NOZZLE **

** Actual enthalpy drop/Isentropic enthalpy drop**

** NOZZLES**

**These are convergent divergent nozzles only. In steam turbines, only super-sonic jets are required to run the high speed turbines.**

**V = **√**2gh**

#### The velocity at inlet of nozzle is much smaller than velocity at outlet. Hence inlet velocity is neglected.

** NOZZLES WITHOUT FRICTION**

**V = 44.72**√**h m/s** **where h is enthalpy drop in k J /kg**

** NOZZLES WITH FRICTION**

**V = 44.72**√**k h m/s**

**k = nozzle friction coefficient or nozzle efficiency, it reduces the enthalpy drop by 10 to 15 %**

#### Therefore value of k = 0.85 to 0.90

**h = isentropic enthalpy drop (k J/kg) in the nozzle**

### ANALYSIS OF NOZZLES

**Velocity ‘v’ in terms of pressure and volume**

**v = √2(n/(n-1))p1V1 [1 –(p2/p1) **^{(n – 1)/n}

**Where p1 and p2 are the pressures at the inlet and outlet of the convergent portion**

**v is the velocity of steam at the throat**

**V1 is the specific volume at the inlet of the convergent portion**

^{(n – 1)/n}

**CONDITION FOR MAXIMUM DISCHARGE THROUGH THE NOZZLE**

**p**_{2}/p_{1} = [2/(n+1)] ^{n/(n-1)}

**FOR SATURATED STEAM, n= 1.135**

**p**_{2}/p_{1}= 0.58

**FOR SUPERHEATED STEAM, n = 1.3**

**p**_{2}/p_{1}= 0.546

_{2}/p

_{1}= [2/(n+1)]

^{n/(n-1)}

_{2}/p

_{1}= 0.58

_{2}/p

_{1}= 0.546

**MAXIMUM FLOW RATE**

**m**^{. }_{max} = A_{t }[n(p_{1}/v_{1})[2/(n+1)] ^{(n+1)/(n-1)}]^{0.5}

**where A**_{t} is the area at throat

**v **_{max} = √(2(n/(n+1))p_{1}V_{1})

**v **_{max} maximum velocity at the throat

^{. }

_{max}= A

_{t }[n(p

_{1}/v

_{1})[2/(n+1)]

^{(n+1)/(n-1)}]

^{0.5}

_{t}is the area at throat

_{max}= √(2(n/(n+1))p

_{1}V

_{1})

_{max}maximum velocity at the throat

**RELATION BETWEEN AREA, VELOCITY AND PRESSURE IN FLOW THROUGH THE NOZZLE**

**dA/A = (1/n)(dp/p)[(1 – M2)/M2]**

**In flow through the nozzle, dp/p is negative—decrease of pressure with increase of length**

**TWO DIFFERENT CASES ARISE**

**CASE 1—ACCELERATED FLOW**—–**REQUIRED IN STEAM TURBINES**

**Two different possibilities arise**

**(i) If v < c, M < 1, where c is the velocity of sound**

**∴dA/A should be negative i.e. area should decrease i.e. CONVERGENT**

**∴ Convergent portion produces sonic velocity.**

**(ii) If v > c, M > 1, ∴dA/A should be positive i.e. area should increase i.e. DIVERGENT**

**∴ Divergent portion produces super sonic velocity.**

**CASE 2 **

**DEACCELERATED FLOW**

**IT IS NOT APPLICABLE TO STEAM NOZZLES**

**Decrease of velocity throughout**

**It will occur in the diffuser**

**dp/p will be positive.**

**V > c , M > 1 **

**dA/A has to be positive—-divergent portion**

**kinetic energy is converted into pressure energy.**

**CASE 2 IS NOT APPLICABLE TO NOZZLES USED IN STEAM TURBINES SINCE ONLY ACCELERATED FLOW IS REQUIRED.**

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