Pump Design

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MATHEMATICS IN ENGINEERING
Pump Design
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MATHEMATICS IN ENGINEERING
Hydraulic Design and Vectors
Cm2
W2
U1
W1
U2
Cm1
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MATHEMATICS IN ENGINEERING
Vectors
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MATHEMATICS IN ENGINEERING
Polynomial Curve Fits
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MATHEMATICS IN ENGINEERING
Polynomial Curve Fits

• 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

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MATHEMATICS IN ENGINEERING
Vibration - Curve Fits ,Trig functions
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MATHEMATICS IN ENGINEERING
Curve Fitting
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MATHEMATICS IN ENGINEERING
Curve Fitting
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MATHEMATICS IN ENGINEERING
Trigonometric Functions
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MATHEMATICS IN ENGINEERING
Trigonometric Functions
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MATHEMATICS IN ENGINEERING
Trigonometric Functions
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MATHEMATICS IN ENGINEERING
Trigonometric Functions
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, w22pf2, q1 and q2 are
phase angles NB. in the example a1 1, a2 0.5
and w22w1
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MATHEMATICS IN ENGINEERING
Stress and Dynamics Matrices and Differential
Equations
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MATHEMATICS IN ENGINEERING
Matrices
CANTILEVER UNDER LOAD AND MOMENT
Moment M Rotation q
L
Load W Deflection d
Calculus to determine I
General matrix equation FKq or
qK-1F
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MATHEMATICS IN ENGINEERING
Differential equations
Equation of free vibration of a pump rotor
including hydraulic forces
Dynamically stable
Dynamically unstable