Vertical Flow in an Expanding Pipe

A vertical pipe carrying water upward within an expanding pipe has pressure gauges inserted at points A and B$.$ The pipe diameters at A and B are $0\mathrm{.}15m$ and $0\mathrm{.}075m,$ respectively. Further, point $B$ is located $2\mathrm{.}5m$ below point $A.$ When the flow in the pipe is $Q=0\mathrm{.}02m^3{s}^{-1},$ the pressure differential $($measured as $p_A-p_B)$ is $15000N{m}^{-2}.$ Assuming energy losses in the pipe between points B and A can be expressed as $k\frac{v^2}{2g}$ where $v$ is the velocity at point $A($yes $...$ I know we have yet to discuss the concept of fluid energy in class but you can still solve this problem$),$ determine the required value for $k$ via application of the Bernoulli equation if we can assume the following:

$\frac{p_A}{g}+\frac{v_A^2}{2g}+z_A=\frac{p_B}{g}+\frac{v_B^2}{2g}+z_B+\frac{k{v}_A^2}{2g}$