A two-dimensional channel of width H has a slot of width h as shown. Fluid is injected through the slot at an angle Psi to the horizontal. The fluid is incompressible with density rho and body forces can be neglected. Assume velocity and pressure are constant across the channel. a Derive an equation governing mass for the channel, b Derive an equation governing x momentum for the channel. c Now, assume Psi = 60 Degree such that cos Psi = 1/2. Combine your results of Parts (a) and (b) with Bernoulli\'s equation to determine U_2 as a function of U_1, H and h. Solution Mass of channel before jiont =pAv 1 A= AREA = H*D D= depth of channel mass of channel after joint = mass before joint + mass added by small channel = pHDV 1 + phD*V MOMENTUM = MASS+ VELOCITY TOTEL MOMENTUM IN X DIRECTION BEFORE JOINT = Â Â pHDV 1 2 + phD*V 2 *Cos velocity of fluid after jiont is = (A 1 V 1 +A 2 V)/A 1 = (HD*V 1 + hDV)/HD = V 1 + hV/H MOMENTUM AFTER JOINT IN X DIRECTION = pHD(V 1 + hV/H) 2 .