Problem $2(10p)$ : A Venturi tube is displayed in the figure. The cross section with the larger diameter is denoted with index $(1),$ and the cross$-$section with the small diameter is denoted with index $(2).$ The diameters of the tubes are $d_1=50mm$ and $d_2=10mm.$ The fluid in the venturi tube is water, and it's pressure difference is measured with a U$-$tube, in which the liquid is mercury. The displacement of the mercury columns us $h=13mm.$ The density of the water and the mercury are ${}_w=1000k\frac{g}{m^3}$ and ${}_m=13600k\frac{g}{m^3},$ respectively. Find the pressure difference measured by the U$-$tube. Calculate the velocities at both cross$-$sections. Calculate the volumetric flow rate aqnd mass flow rate of the fluid.

$\backslash$table$[[p(Pa)(4p),v_1(\frac{m}{s})(2p),v_2(\frac{m}{s})(2p),Q(\frac{m^3}{s})(1p),m^{}k\frac{g}{s}(1p)$