B$1.$ vuestion $B_2$ : A vecy largo water pool is foreseen with a recirculating system consisting of a pipe which provides water at a rase of $m-1m^{\frac{3}{s}}($per unit iength$).$ The pips is located at a distance $a=3m$ from the poot floot. A wher drain is located on the pool floor. The drain can be moselled as a sink of strength $M.$ It dernins all the waser provided by the source $m.$

a$)$ Determine a suitable function to model this flow. Verify that the floor is correctly modelled.

b$)$ What must be the strengit $M$ of the sink used to repersent the drain?

c$)$ The system is monitared by messuring the pressure difference siong the floor of the pool it the location $b=1m$ and $c=2m.$ For the given operating conditions, whas will be this preasuce difference?

For water, use $=1000k\frac{g}{m^3}.$ Negiest gravitational effects.

Figure B$2$: Schematic pool recirculating syssem.