Sir for the first question main formula is D*P=qp*X or P=qp*X ? Because after simplifying qp, the formula you have used here is coming from the 2nd one but I have studied the first formula in some sources. Which one is correct?
The formula I used is derived by simple concept and intuition. Product Yield (Y p/x) is product formation rate divided by amount of substrate consumed. Productivity (the amount of product generated) is given in units g/L/h. This is the 'g' amount of product generated in 1 L in 1 hour, which will be in the numerator. In denominator, one has to think of the substrate consumed. Since this is the continuous culture, we have to see how efficiently cells convert substrate into products under growth-associated conditions. For this, we have to multiply specific growth rate (given in unit 'per hour') with steady state substrate concentration (given in g/L), which describes how rapidly substrate is being consumed per unit of biomass. At the end, after all this, the units do align with the given Yield (g/g), which means the formula is appropriate. For this, one does not need to mug up the formula. If one knows the concept, the formula is easy to derive. I did not refer to any source for this formula. Edit: Solving your confusion about the correctness of the formula. The first formula you mentioned is correct and can be applied here after proper derivation. qp is of value "Y p/x * u". Putting its value in your first formula, we get D*P = Y p/x*u*X. D*P here actually represents productivity and has the same units g/L/h. Rearranging the u*X into the denominator on the other side, we get the same formula as I applied in the question.
Sir for the first question main formula is D*P=qp*X or P=qp*X ? Because after simplifying qp, the formula you have used here is coming from the 2nd one but I have studied the first formula in some sources. Which one is correct?
The formula I used is derived by simple concept and intuition. Product Yield (Y p/x) is product formation rate divided by amount of substrate consumed. Productivity (the amount of product generated) is given in units g/L/h. This is the 'g' amount of product generated in 1 L in 1 hour, which will be in the numerator. In denominator, one has to think of the substrate consumed. Since this is the continuous culture, we have to see how efficiently cells convert substrate into products under growth-associated conditions. For this, we have to multiply specific growth rate (given in unit 'per hour') with steady state substrate concentration (given in g/L), which describes how rapidly substrate is being consumed per unit of biomass. At the end, after all this, the units do align with the given Yield (g/g), which means the formula is appropriate. For this, one does not need to mug up the formula. If one knows the concept, the formula is easy to derive. I did not refer to any source for this formula.
Edit: Solving your confusion about the correctness of the formula. The first formula you mentioned is correct and can be applied here after proper derivation. qp is of value "Y p/x * u". Putting its value in your first formula, we get D*P = Y p/x*u*X. D*P here actually represents productivity and has the same units g/L/h. Rearranging the u*X into the denominator on the other side, we get the same formula as I applied in the question.