Question

A liquid jet with density p and cross-sectional area A strikes a block and splits in two, Figure 3. The upper jet has area aA and exits at an angle 8: the lower jet has area (1-a) A is turned 90" downwards. Velocity V is approximately uniform throughout. Derive expressions for the forces Fy and Fy required to keep the block stationary. Neglect the weight of the fluid. BONUS: Find the values of a and @ for which F = F = 0.(10 points) QA (1-a) A Figure 3. Jet and Block for Question 4.

Answer 1

a usina 2.A woso VO - (1- A fy v I The coordinate axis is attached to fig. The meass flow rate at various secrion: m = EAU S since velocity remains m = e(x.A) { same throug out / m = e(19) AV min Density xarepa velocity are | The veiocity component at various section (VD, 3-v2 (12)z = -ucoso 4 (U3) = 0 CVJy = 0, (Ozdy - s sino ! (V;), = -v

put values the force required to keep hold section use impulse-momentum eq? Fe = (m7,.)z - [eis vele + (ni, vs)x] fre = fear) (-v]-[ie.cn.v) (_vcoso) + Cellular Yo] Fee = - eAvata2.A.222c056 IFR = eau? (x1050-1) AnwOR I g-direction force au use impulse momenta egh in g- direction Fy = (i, Uily - [hizzly + lui V3) y] fy = (enius (0) - [Lema.V) vsino + 261-494V (-03] fy - - ['eau?arsino - eAuzel-ey] D fy - env?(1-) – equeasing M = eau? [e-dj- a sino a force asing in y-direction . 1 Answer

ROLL Values of a and o for which fre=payao fac = equz [x (050-17 o equz [arcoso-1) => 2010 = 1 ->0 Py = cava [(1-) = esines) 0 = equa [21-x)= a sinas] 4 (I-) - a cao so =) a since =ta @ (emoj? 7 (eezzza Casince ²+ (acosal 2 = (+)²+(1-992 =) x² (sinzo+coste) = 1+(1+q² za ) =) = 274-24 24 - 2 Roll Awware in ean put acolo. (2-) coso Coso = Cod O' 102097 Auso To=1 and 0=0 / fe and by care equal to 72 ,