7. As shown in the following liquid-liquid ejector, both of the two streams are the same fluid. Two fluid streams merge at plane 1. Stream la has a velocity vo and a cross-sectional area 1/351, and stream 1b has a velocity 1/2 V and a cross-sectional area 2/351. Plane 2 is chosen far enough downstream that the two streams have mixed and the velocity is almost uniform at v. The flow is turbulent and the velocity profiles at planes 1 and 2 are assumed to be flat.

Assume Fr-s is neglected. Derive the following three equations using mass, momentum and mechanical energy balances.

7. As shown in the following liquid-liquid ejector, both of the two streams are the same fluid. Two fluid streams merge at plane 1 . Stream 1 a has a velocity w0 and a cross-sectional area 1/3S1, and stream 1b has a velocity 1/2v0 and a cross-sectional area 2/3S1. Plane 2 is chosen far enough downstream that the two streams have mixed and the velocity is almost uniform at v2. The flow is turbulent and the velocity profiles at planes 1 and 2 are assumed to be flat. momentum and mechanical energy balances. (15\%) (a) v2=32v0(b)p2p1=181v02(c)Ev=1445v02 Momentum balance: (v1w1+p1S1)u1(v2w2+p2S2)u2+mtotg=Ffs where mtong and Ff, are the force of gravity on fluid and the force of the fluid on the solid surfaces, respectively. Unit vectors u1 and u2 represent the direction of flow at planes 1 and 2 , respectively. Mechanical energy balance: (21v12+gh1+1p1)w1(21v22+gh2+2p2)w2=Wm+Ec+Ev where w is the mass rate of flow passing through any cross section of the flow system, Wm represents the rate of doing work on fluid by moving surfaces, Ec denotes the rate at which mechanical energy increases or decreases because of expansion or compression of fluid, and E v represents the rate at which mechanical energy deereases because of viscous dissipation