2 Ten data points were obtained from a pump test The followi

2. Ten data points were obtained from a pump test. The following set of data represents efficiency versus flow rate: Q = 20; 20; 30; 40; 40; 50; 50; 50; 60; 70 (m3/s) p = 0.73; 0.78; 0.85; 0.90; 0.91; 0.87; 0.86; 0.91; 0.75; 0.65
Fit a quadratic model using a least squares fit to the above data:   p = ao + a1Q + a2Q2 Then, determine the value of \'Q\' in which the maximum pump efficiency occurs.

Solution

The quadratic model using the least square fit is given by;

p = 0.3566 + 0.0263 Q - 0.0003 Q^2

The solution to this equation is ( 99.609, -11.934)

Thus it is clear that the maximum pump efficiency occurs at Q = 99.