Function VELOCITY

• Defined in theory: Thermal-system
• Source code: thermal-system.ol

Slots on this function:

Documentation:

the velocity of the fluid through the stream

Instance-Of: Function, Quantity-function

Arity: 2

Range: Everywhere-continuous-quantity

Other Related Axioms:

(Inherited-Facet-Value Slot-Documentation
                       Stream
                       Velocity
                       The Velocity Of The Fluid Through The Stream)

(Quantity.Dimension (Velocity ?Self) Velocity-Dimension)

(Inherited-Facet-Value Slot-Cardinality Stream Velocity 1)

(Has-Quantity-Function Stream Velocity)

(Slot-Documentation Stream
                    Velocity
                    The Velocity Of The Fluid Through The Stream)

(=> (Stream ?Self)
    (And (Value-Cardinality ?Self Stream-Elevation 1)
         (Quantity.Dimension (Stream-Elevation ?Self)
                             Length-Dimension)
         (Value-Cardinality ?Self Enthalpy-Rate 1)
         (Quantity.Dimension (Enthalpy-Rate ?Self) Power-Dimension)
         (Value-Cardinality ?Self Entropy-Rate 1)
         (Quantity.Dimension (Entropy-Rate ?Self)
                             Entropy-Rate-Dimension)
         (Value-Cardinality ?Self Ke-Rate 1)
         (Quantity.Dimension (Ke-Rate ?Self) Power-Dimension)
         (Value-Cardinality ?Self Mass-Rate 1)
         (Quantity.Dimension (Mass-Rate ?Self) Mass-Rate-Dimension)
         (Value-Cardinality ?Self Pe-Rate 1)
         (Quantity.Dimension (Pe-Rate ?Self) Power-Dimension)
         (Value-Cardinality ?Self Stream-Pressure 1)
         (Quantity.Dimension (Stream-Pressure ?Self)
                             Pressure-Dimension)
         (Value-Cardinality ?Self Specific-Enthalpy 1)
         (Quantity.Dimension (Specific-Enthalpy ?Self)
                             Specific-Energy-Dimension)
         (Value-Cardinality ?Self Specific-Entropy 1)
         (Quantity.Dimension (Specific-Entropy ?Self)
                             Specific-Entropy-Dimension)
         (Value-Cardinality ?Self Specific-Internal-Energy 1)
         (Quantity.Dimension (Specific-Internal-Energy ?Self)
                             Specific-Energy-Dimension)
         (Value-Cardinality ?Self Stream-Temperature 1)
         (Quantity.Dimension (Stream-Temperature ?Self)
                             Temperature-Dimension)
         (Value-Cardinality ?Self Velocity 1)
         (Quantity.Dimension (Velocity ?Self) Velocity-Dimension)
         (Value-Cardinality ?Self Quality 1)
         (Quantity.Dimension (Quality ?Self) Dimensionless)
         (Value-Cardinality ?Self Specific-Volume 1)
         (Quantity.Dimension (Specific-Volume ?Self)
                             Specific-Volume-Dimension)
         (Value-Cardinality ?Self Saturated-P 1)))

(=> (Velocity $X $Y) (Everywhere-Continuous-Quantity $Y))

(Forall 
    (?Self ?Time)
    (=> (Active ?Time 2d-Stream-Mass-Flow-Rate ?Self)
        (= (* (Lambda (?T)
                      (If (= ?T ?Time)
                          (Value-At (Mass-Rate 
                                        (2d-Stream-Involved ?Self))
                                    ?T)))
              (Lambda 
                  (?T)
                  (If (= ?T ?Time)
                      (Value-At 
                          (Specific-Volume (2d-Stream-Involved ?Self))
                          ?T))))
           (* (Lambda (?T)
                      (If (= ?T ?Time)
                          (Value-At 
                              (Stream-Area (2d-Stream-Involved ?Self))
                              ?T)))
              (Lambda (?T)
                      (If (= ?T ?Time)
                          (Value-At (Velocity (2d-Stream-Involved ?Self))
                                    ?T)))))))

(Forall 
    (?Self ?Time)
    (=> (Active ?Time 2d-Stream-Kinetic-Energy ?Self)
        (= (Lambda (?T)
                   (If (= ?T ?Time)
                       (Value-At (Ke-Rate (2d-Stream-Involved ?Self))
                                 ?T)))
           (* 0.5
              (Lambda (?T)
                      (If (= ?T ?Time)
                          (Value-At (Mass-Rate 
                                        (2d-Stream-Involved ?Self))
                                    ?T)))
              (Expt (Lambda 
                        (?T)
                        (If (= ?T ?Time)
                            (Value-At 
                                (Velocity (2d-Stream-Involved ?Self))
                                ?T)))
                    2)))))