Equation of motion for steady flow with friction and machines (i.e. pumps or turbines ) Recall (Energy per unit weight)

Equation of motion for steady flow with friction and machines (i.e. pumps or turbines ) Recall (Energy per unit weight) For flow with no friction nor machines (Bernoulli’s equation between sections 1 and 2)

Equation of motion for steady flow with friction and machines (i.e. pumps or turbines ) Recall (Energy per unit weight) For flow with no friction nor machines (Bernoulli’s equation between sections 1 and 2) For flow with friction and no machines (assuming flow goes from section 1 to section 2) is the pipe friction head loss

Equation of motion for steady flow with friction and machines (i.e. pumps or turbines ) Recall (Energy per unit weight) For flow with no friction nor machines (Bernoulli’s equation between sections 1 and 2) For flow with friction and no machines (assuming flow goes from section 1 to section 2) For flow with friction and machines (assuming flow goes from section 1 to section 2) is the head gain or loss associated with machine is the pipe friction head loss

Equation of motion for steady flow with friction and machines (i.e. pumps or turbines ) Assuming flow goes from section 1 to section 2

If the machine is a pump,, where is the energy head put into the flow by the pump Equation of motion for steady flow with friction and machines (i.e. pumps or turbines ) Assuming flow goes from section 1 to section 2

If the machine is a pump,, where is the energy head put into the flow by the pump If the machine is a turbine,, where is the energy extracted from the flow by the turbine Equation of motion for steady flow with friction and machines (i.e. pumps or turbines ) Assuming flow goes from section 1 to section 2

Power When dealing with turbines or pumps, engineers often speak in terms of power Power is defined as the rate of transfer of energy

Power When dealing with turbines or pumps, engineers often speak in terms of power Power is defined as the rate of transfer of energy

Power When dealing with turbines or pumps, engineers often speak in terms of power Power is defined as the rate of transfer of energy To find power extracted from a flow by a turbine, we let in equation above

Power When dealing with turbines or pumps, engineers often speak in terms of power Power is defined as the rate of transfer of energy To find power extracted from a flow by a turbine, we let in equation above To find power added to a flow by a pump, we let in equation above

Power When dealing with turbines or pumps, engineers often speak in terms of power Power is defined as the rate of transfer of energy To find power extracted from a flow by a turbine, we let in equation above To find power associated with a jet, say at a discharge, let in equation above where V is the discharge velocity To find power added to a flow by a pump, we let in equation above

Units of power English: 1 hp = 1 Horsepower = 550 ft lb/sec SI: 1 KW = 1 Kilowatt = 1 m kN/s

Units of power English: 1 hp = 1 Horsepower = 550 ft lb/sec SI: 1 KW = 1 Kilowatt = 1 m kN/s Efficiency of machines Efficiency:

Example: Exercise (Pump) Pump Oil (S=0.82) Flow Want: Rate at which energy is delivered to oil by pump

Example: Exercise (Pump) Pump Oil (S=0.82) Flow Want: Rate at which energy is delivered to oil by pump

Example: Exercise (Pump) Pump Oil (S=0.82) Flow Want: Rate at which energy is delivered to oil by pump Need to find h p associated with the pump:

Example: Exercise (Pump)

Rate of transfer of energy =

Example: Exercise (Pump) Pumps (and also turbines) are characterized by their efficiency

Example: Exercise (Pump) Pumps (and also turbines) are characterized by their efficiency Say, in exercise the pump is 90% efficient and we require 6.83 kW of output, then input = 6.83 kW / 0.9 = 7.59 kW

Example: Exercise (Pump) Pumps (and also turbines) are characterized by their efficiency Say, in exercise the pump is 90% efficient and we require 6.83 kW of output, then input = 6.83 kW / 0.9 = 7.59 kW Pumps (and also turbines) are characterized by their efficiency. Efficiency =

General Energy Equation for Steady Flow of Any Fluid First Law of Thermodynamics: For steady flow, external work done on any system plus the thermal energy transferred into or out of the system is equal to the change of energy of the system

General Energy Equation for Steady Flow of Any Fluid First Law of Thermodynamics: For steady flow, external work done on any system plus the thermal energy transferred into or out of the system is equal to the change of energy of the system (I) Using the first law of thermodynamics, (II) taking into account non-uniform velocity at a cross-section of flow region, and (III) assuming flow goes from section 1 to section 2, we can derive the following:

General Energy Equation for Steady Flow of Any Fluid is a correction factor accounting for non-uniform velocity in cross-section If velocity is uniform in cross-section, then

General Energy Equation for Steady Flow of Any Fluid is a correction factor accounting for non-uniform velocity in cross-section If velocity is uniform in cross-section, then This general equation also takes into account changes in density (via ) energy changes due to machines (via ) and energy changes due to heat transfer to or from outside the fluid (via )

General Energy Equation for Steady Flow of Any Fluid is a correction factor accounting for non-uniform velocity in cross-section If velocity is uniform in cross-section, then It also accounts for the conversions of other forms of fluid energy into internal energy ( ) internal energy per unit weight = This general equation also takes into account changes in density (via ) energy changes due to machines (via ) and energy changes due to heat transfer to or from outside the fluid (via )

General Energy Equation for Steady Flow of Any Fluid On a unit weight basis, the change in internal energy is equal to the heat added to or removed from the fluid plus the heat generated by fluid friction:

General Energy Equation for Steady Flow of Any Fluid On a unit weight basis, the change in internal energy is equal to the heat added to or removed from the fluid plus the heat generated by fluid friction: The head loss due to friction is equal to the internal heat gain minus any heat added from external sources, per unit weight of fluid

General Energy Equation for Steady Flow of Any Fluid On a unit weight basis, the change in internal energy is equal to the heat added to or removed from the fluid plus the heat generated by fluid friction: The head loss due to friction is equal to the internal heat gain minus any heat added from external sources per unit weight of fluid and becomes

General Energy Equation for Steady Flow of Any Fluid Energy loss due to friction gets converted to internal energy (proportional to temperature)