Slide1 : Pump Design MATHEMATICS IN ENGINEERING
Slide2 : U1 U2 W1 W2 Cm1 Cm2 Hydraulic Design and Vectors MATHEMATICS IN ENGINEERING
Slide3 : MATHEMATICS IN ENGINEERING
Vectors
Slide4 : MATHEMATICS IN ENGINEERING Polynomial Curve Fits
Slide5 : MATHEMATICS IN ENGINEERING
Fit hydraulic performance curve data Head and Flow Q
Head dependency with impeller diameter and flow
A seventh order polynomial fit of generated head versus flow
where the each coefficient ai is given by:-
A fifth order polynomial fit used for the coefficients as a function of impeller diameter, where:-
and Q is flowrate and Di are diameters , i =1, 5 Polynomial Curve Fits
Slide6 : Vibration - Curve Fits ,Trig functions MATHEMATICS IN ENGINEERING
Slide7 : MATHEMATICS IN ENGINEERING Curve Fitting
Slide8 : MATHEMATICS IN ENGINEERING Curve Fitting
Slide9 : MATHEMATICS IN ENGINEERING Trigonometric Functions
Slide10 : MATHEMATICS IN ENGINEERING Trigonometric Functions
Slide11 : MATHEMATICS IN ENGINEERING Trigonometric Functions
Slide12 : MATHEMATICS IN ENGINEERING
The composite vibration is made up of two sine waves of amplitude a1 and a2 and time period T1 and T2 with corresponding frequencies f1 and f2 where
f1 =1/ T1 and f2 =1/T2
Mathematically the complex periodic wave form can be written as
F(t)= a1sin(w1t +q1) + a2 sin(w2t +q2)
Where w1 =2pf1, w2=2pf2, q1 and q2 are phase angles
NB. in the example a1 =1, a2 =0.5 and w2=2w1 Trigonometric Functions
Slide13 : Stress and Dynamics – Matrices and Differential Equations MATHEMATICS IN ENGINEERING
Slide14 : Load W
Deflection d Moment M
Rotation q CANTILEVER UNDER LOAD AND MOMENT L MATHEMATICS IN ENGINEERING
Matrices General matrix equation ={F}=[K]{q} or {q}=[K]-1{F} Calculus to determine I
Slide15 : MATHEMATICS IN ENGINEERING Dynamically stable Dynamically unstable
Equation of free vibration of a pump rotor
including hydraulic forces Differential equations