Vapor Pressure, Viscosity, Cavitations

1 VAPOR PRESSURE, VISCOSITY, CAVITATIONS

VAPOUR PRESSURE
Liquids exhibit a free surface in the container whereas vapours and gases fill the full volume. Liquid molecules have higher cohesive forces and are bound to each other. In the gaseous state the binding forces are minimal. Molecules constantly escape out of a liquid surface and an equal number constantly enter the surface when there is no energy addition. The number of molecules escaping from the surface or re-entering will depend upon the temperature. Under equilibrium conditions these molecules above the free surface exert a certain pressure. This pressure is known as vapour pressure corresponding to the temperature. As the temperature increases, more molecules will leave and re-enter the surface and so the vapour pressure increases with temperature. All liquids exhibit this phenomenon. Sublimating solids also exhibit this phenomenon. The vapour pressure is also known as saturation pressure corresponding to the temperature. The temperature corresponding to the pressure is known as saturation temperature. If liquid is in contact with vapour both will be at the same temperature and under this condition these phases will be in equilibrium unless energy transaction takes place. The vapour pressure data for water and refrigerants are available in tabular form. The vapour pressure increases with the temperature. For all liquids there exists a pressure above which there is no observable difference between the two phases. This pressure is known as critical pressure. Liquid will begin to boil if the pressure falls to the level of vapour pressure corresponding to that temperature. Such boiling leads to the phenomenon known as cavitation in pumps and turbines. In pumps it is usually at the suction side and in turbines it is usually at the exit end.
1.12.1 Partial Pressure
In a mixture of gases the total pressure P will equal the sum of pressures exerted by each of the components if that component alone occupies the full volume at that temperature. The pressure exerted by each component is known as its partial pressure.
P = p1 +p2 + p3 + ....
where p1 = (m1R1T)/V ; p2 = (m2R2T)/V in which T and V are the common temperature and volume. For example air is a mixture of various gases as well as some water vapour. The atmospheric pressure is nothing but the sum of the pressures exerted by each of these components. Of special interest in this case is the partial pressure of water vapour. This topic is studied under Psychrometry. The various properties like specific heat, gas constant etc. of the mixture can be determined from the composition.
cm = Σ (ci × mi)/Σmi
where cm is the specific heat of the mixture and ci and mi are the specific heat and the mass of component i in the mixture.

Viscosity and Momentum Transfer
In the flow of liquids and gases molecules are free to move from one layer to another. When the velocity in the layers are different as in viscous flow, the molecules moving from the layer at lower speed to the layer at higher speed have to be accelerated. Similarly the molecules moving from the layer at higher velocity to a layer at a lower velocity carry with them a higher value of momentum and these are to be slowed down. Thus the molecules diffusing across layers transport a net momentum introducing a shear stress between the layers. The force will be zero if both layers move at the same speed or if the fluid is at rest. When cohesive forces exist between atoms or molecules these forces have to be overcome, for relative motion between layers. A shear force is to be exerted to cause fluids to flow. Viscous forces can be considered as the sum of these two, namely, the force due to momentum transfer and the force for overcoming cohesion. In the case of liquids, the viscous forces are due more to the breaking of cohesive forces than due to momentum transfer (as molecular velocities are low). In the case of gases viscous forces are more due to momentum transfer as distance between molecules is larger and velocities are higher.
Effect of Temperature on Viscosity
When temperature increases the distance between molecules increases and the cohesive force decreases. So, viscosity of liquids decrease when temperature increases. In the case of gases, the contribution to viscosity is more due to momentum transfer. As temperature increases, more molecules cross over with higher momentum differences. Hence, in the case of gases, viscosity increases with temperature.
Significance of Kinematic Viscosity
Kinematic viscosity, ν = μ/ρ , The unit in SI system is m2/s. (Ns/m2) (m3/ kg) = [(kg.m/s2) (s/m2)] [m3/kg] = m2/s Popularly used unit is stoke (cm2/s) = 10–4 m2/s named in honour of Stokes. Centi stoke is also popular = 10–6 m2/s.
Kinematic viscosity represents momentum diffusivity.

τ = μ (du/dy) = (μ/ρ) × {d (ρu/dy)} = ν × {d (ρu/dy)}
d (ρu/dy) represents momentum flux in the y direction.
So, (μ/ρ) = ν kinematic viscosity gives the rate of momentum flux or momentum diffusivity. With increase in temperature kinematic viscosity decreases in the case of liquids and increases in the case of gases. For liquids and gases absolute (dynamic) viscosity is not influenced significantly by pressure. But kinematic viscosity of gases is influenced by pressure due to change in density. In gas flow it is better to use absolute viscosity and density, rather than tabulated values of kinematic viscosity, which is usually for 1 atm.

CAVITATION
What is cavitation and where and why it occurs has been discussed in the chapter on turbines.
In the case of pumps, the pressure is lowest at the inlet and cavitation damage occurs
at the inlet. For cavitation to occur the pressure at the location should be near the vapour
pressure at the location.
Applying the energy equation between sump surface and the pump suction,
P_s/γ+ (V_s^2)/2g+Z= P_a/γ-h_fs
where Z is the height from sump surface and pump suction. The other terms have their usual
significance. The term hfs should include all losses in the suction line.
Net Positive Suction Head (NPSH) is defined as the available total suction head at the pump inlet above the head corresponding to the vapour pressure at that temperature.
VAPOUR PRESSURE
Liquids exhibit a free surface in the container whereas vapours and gases fill the full volume. Liquid molecules have higher cohesive forces and are bound to each other. In the gaseous state the binding forces are minimal. Molecules constantly escape out of a liquid surface and an equal number constantly enter the surface when there is no energy addition. The number of molecules escaping from the surface or re-entering will depend upon the temperature. Under equilibrium conditions these molecules above the free surface exert a certain pressure. This pressure is known as vapour pressure corresponding to the temperature. As the temperature increases, more molecules will leave and re-enter the surface and so the vapour pressure increases with temperature. All liquids exhibit this phenomenon. Sublimating solids also exhibit this phenomenon. The vapour pressure is also known as saturation pressure corresponding to the temperature. The temperature corresponding to the pressure is known as saturation temperature. If liquid is in contact with vapour both will be at the same temperature and under this condition these phases will be in equilibrium unless energy transaction takes place. The vapour pressure data for water and refrigerants are available in tabular form. The vapour pressure increases with the temperature. For all liquids there exists a pressure above which there is no observable difference between the two phases. This pressure is known as critical pressure. Liquid will begin to boil if the pressure falls to the level of vapour pressure corresponding to that temperature. Such boiling leads to the phenomenon known as cavitation in pumps and turbines. In pumps it is usually at the suction side and in turbines it is usually at the exit end.
1.12.1 Partial Pressure
In a mixture of gases the total pressure P will equal the sum of pressures exerted by each of the components if that component alone occupies the full volume at that temperature. The pressure exerted by each component is known as its partial pressure.
P = p1 +p2 + p3 + ....
where p1 = (m1R1T)/V ; p2 = (m2R2T)/V in which T and V are the common temperature and volume. For example air is a mixture of various gases as well as some water vapour. The atmospheric pressure is nothing but the sum of the pressures exerted by each of these components. Of special interest in this case is the partial pressure of water vapour. This topic is studied under Psychrometry. The various properties like specific heat, gas constant etc. of the mixture can be determined from the composition.
cm = Σ (ci × mi)/Σmi
where cm is the specific heat of the mixture and ci and mi are the specific heat and the mass of component i in the mixture.

Viscosity and Momentum Transfer
In the flow of liquids and gases molecules are free to move from one layer to another. When the velocity in the layers are different as in viscous flow, the molecules moving from the layer at lower speed to the layer at higher speed have to be accelerated. Similarly the molecules moving from the layer at higher velocity to a layer at a lower velocity carry with them a higher value of momentum and these are to be slowed down. Thus the molecules diffusing across layers transport a net momentum introducing a shear stress between the layers. The force will be zero if both layers move at the same speed or if the fluid is at rest. When cohesive forces exist between atoms or molecules these forces have to be overcome, for relative motion between layers. A shear force is to be exerted to cause fluids to flow. Viscous forces can be considered as the sum of these two, namely, the force due to momentum transfer and the force for overcoming cohesion. In the case of liquids, the viscous forces are due more to the breaking of cohesive forces than due to momentum transfer (as molecular velocities are low). In the case of gases viscous forces are more due to momentum transfer as distance between molecules is larger and velocities are higher.
Effect of Temperature on Viscosity
When temperature increases the distance between molecules increases and the cohesive force decreases. So, viscosity of liquids decrease when temperature increases. In the case of gases, the contribution to viscosity is more due to momentum transfer. As temperature increases, more molecules cross over with higher momentum differences. Hence, in the case of gases, viscosity increases with temperature.
Significance of Kinematic Viscosity
Kinematic viscosity, ν = μ/ρ , The unit in SI system is m2/s. (Ns/m2) (m3/ kg) = [(kg.m/s2) (s/m2)] [m3/kg] = m2/s Popularly used unit is stoke (cm2/s) = 10–4 m2/s named in honour of Stokes. Centi stoke is also popular = 10–6 m2/s.
Kinematic viscosity represents momentum diffusivity.

τ = μ (du/dy) = (μ/ρ) × {d (ρu/dy)} = ν × {d (ρu/dy)}
d (ρu/dy) represents momentum flux in the y direction.
So, (μ/ρ) = ν kinematic viscosity gives the rate of momentum flux or momentum diffusivity. With increase in temperature kinematic viscosity decreases in the case of liquids and increases in the case of gases. For liquids and gases absolute (dynamic) viscosity is not influenced significantly by pressure. But kinematic viscosity of gases is influenced by pressure due to change in density. In gas flow it is better to use absolute viscosity and density, rather than tabulated values of kinematic viscosity, which is usually for 1 atm.

CAVITATION
What is cavitation and where and why it occurs has been discussed in the chapter on turbines.
In the case of pumps, the pressure is lowest at the inlet and cavitation damage occurs
at the inlet. For cavitation to occur the pressure at the location should be near the vapour
pressure at the location.
Applying the energy equation between sump surface and the pump suction,
P_s/γ+ (V_s^2)/2g+Z= P_a/γ-h_fs
where Z is the height from sump surface and pump suction. The other terms have their usual
significance. The term hfs should include all losses in the suction line.
Net Positive Suction Head (NPSH) is defined as the available total suction head at the pump inlet above the head corresponding to the vapour pressure at that temperature.