Water in an irrigation ditch of width $$w = 3.22 m$$ and depth $$d= 1.04 m$$ flows with a speed of $$0.207$$ m/s. The mass flux of the flowing water through an imaginary surface is the product of the water’s density ($$1000 kg/m_3$$ ) and its volume flux through that surface. Find the mass flux through the following imaginary surfaces: (a) a surface of area wd, entirely in the water, perpendicular to the flow; (b) a surface with area $$3wd/2$$, of which wd is in the water, perpendicular to the flow; (c) a surface of area $$wd/2$$, entirely in the water, perpendicular to the flow; (d) a surface of area wd, half in the water and half out, perpendicular to the flow; (e) a surface of area wd, entirely in the water, with its normal $$34.0°$$ from the direction of flow.
