Question $3(10$ pts$).$ In a left ventricular assist pump, the pressure head $P$ developed across the

device is given by the following empirical relationship:

$P=c_0+c_1{Q}_P^3+c_2{}^2$

where $$ is the angular velocity of the pump impeller in units of $rad{s}^{-1}$ and $Q_P$ is the pump flow

rate in $m^3{s}^{-1}.$ If $P$ is in units of $)=(N{m}^{-2},$ find the dimensions and units of the coefficients $c_0,$

$c_1$ and $c_2.$Question $3(10$ pts$).$ In a left ventricular assist pump, the pressure head $P$ developed across the

device is given by the following empirical relationship:

$P=c_0+c_1{Q}_P^3+c_2{}^2$

where $$ is the angular velocity of the pump impeller in units of $rad{s}^{-1}$ and $Q_P$ is the pump flow

rate in $m^3{s}^{-1}.$ If $P$ is in units of $)=(N{m}^{-2},$ find the dimensions and units of the coefficients $c_0,$

$c_1$ and $c_2.$