Question

(Fluid mechanics)

2 of 3 Water, assumed inviscid and incompressible, flows steadily out of a large tank as shown in the adjacent figure. Above the water there is a 2-m layer of oil of specific gravity SG = 0.81 and the water outlet is located 0.7 m below the oil-water interface. Take the elevation reference (z = 0) at the outlet level. Determine: Oil, SG = 0.81 0.7 m Water 50 mm diameter a) Are the validity conditions of Bernoulli's equation satisfied? b) Write Bernoulli's equation between point (1) @ the free oil surface and point (2) @ the oil-water interface. c) Show that the above equation reduces to a simple hydrostatic pressure relationship between (1) and (2): P2 = pi + (SG oil water)(g) (hot), where hoit = 2 m. d) Write Bernoulli's equation between (2) @ the oil-water interface and (3) where the jet exits into the atmosphere. e) Show that the exit water jet velocity is: V3 = [29((SG) (hot) + hwater))", where hoi = 2 m and hwater = 0.7 m. Use water = 1000 kg/m and g = 10 m/s? Hint/s): the pressure above the oil and at the ret exit is Dam U

Answer 1

Solution :- Given data! Specific Gravity of oil = 0.81: (a) conditions to apply Bernoulli's equation are (1) Inviscous (11) Incompressible Coni) Steady Torim Z=07 (iv) Irrotational flows. ☺ wala All are satisfied · Henie Bernoulli's equation can be applied (b) Bernoulli's equation between point 0 8 . Piv² + z = P2 + V2 ² + 22.-0 where P,B2 galpressure at poenas 0 @@ . - density of glucid. VI, V2 - velocity of fluid 21,22 - distance from datum Since it is a leerge tank and atmospheric pressure is acting on the suyuce , Pi= 0 (Pathon faken as zero uhen teking' Gauge pressure) V=N1=0 (static fluid) 21=2.7m. Soil - SGoie x Swater = 0«Stx1000 = 810 kg/m3 22 =. 0.7m.

Equation becomes 11.2 ++22 har 21-22 - PB - © P2 = (2.7-2.1) x 810 x 10 = 16200 Pa Pressure at point ®, P2. = Pressvere at point 0 + Hy drastetic pressure applied by oil at poene © P2. = . Pi + [soie xgx hoie P2 = P, + [[sabiex Swader* gx hoie] – Pi - Patmzoears be taken since point o is free surface. Equation ® becomes hole = P2 32-21 = hoil. P2 = (SGDoie x Swader x gx hoie. Hence Equation & - are same Bernoullis Cequation between poenit @ $0. (d) P2 = Swades xg + N2² I G + 2 = PK 7 Swalex9 + 29 + 43 P3 = Palm =0., 73 = clatum = 0.

(e) We know that, P2 = (scDoie Swater x g shoie from Then Equation ③ becomes, equation , (36) id. Swater glx hoir + Z2 = V3 - Sugher xg Z2 = huales → (Sadie xhoie + huaden - vz? Site pet 13 = {zg[esaurulmua) thudte)}"