b$)$ A $1500L$ bioreactor is run with a stirrer speed of $500rpm$ which gives a $k_L$ a value of $800h^{-}$

Calculate the stirrer speed and the motor power required to increase the value of $k_L$ a to

$1000h^{-1}$ at constant aeration rate? Use the following equations to solve the problem..

$P_0=N_p{N}^3{D}_f^5,(1)$

$P_g=k_1(\frac{P_0^{2}N{D}_i^3}{Q^{0\mathrm{.}56}}{)}^{0\mathrm{.}45}$

$K_{L}a=k_2(\frac{P_g}{V}{)}^{0\mathrm{.}67}(v_s{)}^{}$