Scale up of Bacterial growth from 250mL to 1-5L?
Michaelis-Menten: 

$V=V_{max}.\frac{[S]}{Ks+[S]}$

Lineweaver-Burk: 

$\frac{1}{V}=\frac{Ks}{V_{max}[S]}+\frac{1}{V_{max}}$ 

Plot $\frac{1}{V}$ vs $\frac{1}{[S]}$; find the slope and intercept of this plot.

Depending on what you consider as primary substrate (glucose??) measure the concentrations using appropriate assays. Glucose sensors (based on glucose oxidase) are available or you can do conventional biochemical assays (DNSA) for glucose and other reducing sugars. To find the growth rate, measure OD at different time-points and get the differences of OD in a time interval. A better method would be to make a scatter-plot of OD and time and fit a polynomial function. Get rate by taking the tangent of the curve at that time-point.