The measurement of nutrient uptake by microalgae grown in wastewater can be determined by analyzing the concentration of nutrients in the growth medium before and after the algae cultivation. This can be done using techniques such as spectrophotometry or colorimetry, which can determine the nutrient concentrations of the growth medium. This report can be a good start: Technical Report Algae Strain Identification for Wastewater Treatment
Another method for measuring nutrient uptake by microalgae is to track the growth rate of the algae as a function of nutrient availability. This can be done by varying the concentration of a particular nutrient in the growth medium and measuring the resulting growth rate of the algae. This paper can be a useful resource: Article Using Microalgae for Treating Wastewater
The nutrient uptake in algal biomass can be measured using techniques such as combustion analysis, where the algal biomass is burned and the resulting ash is analyzed for nutrient content. Other techniques such as X-ray fluorescence spectroscopy and inductively coupled plasma atomic emission spectroscopy (ICP-AES) can also be used to measure nutrient content in algal biomass.
Overall, the choice of method for measuring nutrient uptake in microalgae will depend on the specific nutrients being studied, the growth conditions, and the analytical equipment available.
It will probably be much easier and more informative to measure the change in the water. Look for a book called " Standard Methods for the Examination of Water and Wastewater" for protocols, or simply google protocols for specific nutrients.
Microalgae can be taken nourishment in domestic wastewater due to containing the nitrate, phosphate. Other alternative, you can cultivate by chemicals, a host of vitamin. Also, light, CO2 concentration and oxygen to be required for their live.