Significance of Critical Pressure Ratio

*Consider a nozzle which connects vessel V_A and V_B. The vessel V_A contains steam at high pressure P_1. The vessel V_B contains steam but its pressure P₂ can be varied based on requirements.

*Initially the pressure P₂ be equal to the pressure P₁ in vessel V_A. By that time, there is no flow through nozzle.

*If the pressure P₂ is gradually reduced in vessel V_B, the discharge through the nozzle increases gradually.

*The pressure P₂, at which the discharge is maximum is called critical pressure.

*If the pressure P₂ is reduced further, the discharge through the nozzle will not increase and it remains at constant level.

* Hence it is confirmed that, at critical pressure ratio, the flow will be maximum.

*The velocity of steam at critical pressure is equal to sonic velocity. This condition will exist at throat cross section of the Convergent divergent nozzle.

Note;

*For convergent – Divergent nozzle, the flow of steam in the convergent portion of the nozzle is subsonic. i.e., the velocity of steam in the convergent section is less than the sound velocity.

*The steam flows in the divergent part of the nozzle is supersonic, i.e., the velocity of the steam in divergent portion is greater than velocity of sound.

Point of Contraflexure

# If the end portion of a beam extends beyond the support, the beam is known as overhanging beam.

Overhanging Beam

# In overhanging beams, the Bending Moment* is positive between the supports, whereas the Bending Moment is negative for overhanging portion.

# At some point on the beam, the B.M is zero after changing its sign from positive to negative or vice-versa.

# That point is known as the point of inflexion or point of contraflexure.

Note:

* Bending Moment (B.M): Algebraic sum of the moments of all the forces acting to the left or right of the section gives bending moment.

Two Reversible Adiabatic Paths Cannot Intersect Each Other

# Let us consider two reversible adiabatic paths 1-3 and 2-3 intersect each other at point 3. 

# Also a reversible constant temperature processes 1-2 be drawn in such a way that it intersects the reversible adiabatic paths at 1 and 2.

# These three reversible processes 1-2, 2-3, 3-1 constitutes a reversible cycle.

# We know that the area under the p-v plot represents the net work output in a cycle. Therefore the area under the three reversible paths represents the net work output in a cycle.

# But such a cycle is not possible, since net work is being produced ia a cycle by a heat engine by exchanging heat with a single reservoir in the processes 1-2, violates the Law of Thermodynamics (Kelvin-Plank). Therefore the consideration of the intersection of the two reversible adiabatic process is wrong.

# Through one point, only one reversible adiabatic can pass.

# As two constant property lines can never intersect each other, it is observed that a reversible adiabatic path must denote some property, which is found later that it is entropy.