An incompressible liquid flows through a pipe as shown in the picture below. One end has a

cross$-$sectional area $A_1=10\mathrm{.}0c{m}^2$ and the other end a cross$-$sectional area $A_2=40\mathrm{.}0c{m}^2.$

Water enters the pipe with a speed $v_1=5\mathrm{.}00{10}^{-2}\frac{m}{s}.$ Calculate the following:

a$.$ The flow speed at the wide portion of the pipe, $v_2.$

b$.$ The pressure difference between the narrow and wide portions of the pipe if the narrow end

is $10cm$ lower than the wide end?