Question $2.$

a$)$ A pump is fitted with a variable speed motor. At $1200$ rpm it delivers $0\mathrm{.}12\frac{m^3}{s}$ of water. What speed of rotation would be required to increase the discharge to $0\mathrm{.}15\frac{m^3}{s}.$

b$)$ A pump has a variable speed motor. At $1000$ rpm the head over which the pump can lift a given quantity of water is $8$ m $.$ If the lift has to be increased to $12$ m $,$ what speed should the pump now run at$?$