b$)$ A dynamic pressure pump transmits $100li\frac{t}{s}$ of water from a tank where the suction level is $3$ m above pump level, to another tank. The suction pipe is $50$ m long, $"f"=0\mathrm{.}04.$ The pump runs at $2000$ rpm at a total head of $6$ m $.$ The vapor and atmospheric pressure are $0\mathrm{.}3$ and $10\mathrm{.}3m$ water. Calculate: the minimum permissible diameter of the suction pipe. Neglect minor losses.

$\backslash$table$[[$Sp$.$ Speed $\{\frac{rpm(\frac{m^3}{s}{)}^{0\mathrm{.}5}}{m^{\frac{3}{4}}}\},28,69,110,165,220],[$Cavitation factor,$0\mathrm{.}1,0\mathrm{.}35,0\mathrm{.}65,1\mathrm{.}1,1\mathrm{.}6]]$