DATA: Consider ${}_{\text{w}\text{a}\text{t}\text{e}\text{r}}=9\mathrm{.}81k\frac{N}{m^3}$ and $g=9\mathrm{.}81\frac{m}{s^2}$

A centrifugal water pump is designed for a rated capacity of $11\frac{L}{s}$ at a total head of $50$ meters. The figure below $($not drawn to scale$)$ shows the main dimensions of the impeller. Assuming that the fluid enters the impeller with no whirl when operating at the design point, determine the following:

a$)$ sketch the velocity triangle at impeller inlet

b$)$ the pump rated speed, $N,$

$(10$ Marks$)$

c$)$ the vane angle at inlet, ${}_1,$ and

d$)$ the actual flow velocity at impeller exit, $U_2^{\text{'}}.$

$1000L=1m^3$

$11\frac{(L)}{(s)}\frac{1m^3}{1000(L)}=0\mathrm{.}011\frac{m^3}{(s)}$

$[$NOTE: If needed consider ${}_{\text{v}\text{a}\text{n}\text{e}}=0\mathrm{.}90,{}_{hyd}=0\mathrm{.}80,{}_{\text{v}\text{o}\text{l}}=0\mathrm{.}96]$

$y_1=u_{1}tan({}_1)$