Question

Question 5 (8 marks) The cart in Figure 1 moves at constant velocity V, and takes on water with a scoop of width B that dips h into a pond (the width B is normal to the paper). The fluid velocity in the pond is v=0. Neglect air drag and wheel friction. The aim is to estimate the force required to keep the cart moving. Assume density is constant. (i) Select a C.V. and clearly indicate w, v and n at all control surfaces. (Note: you may use the recommended C.V. shown in Figure 2. However, you are free to choose another C.V. if you wish.) [2 marks] (ii) Is this steady or unsteady flow? Explain. [1 mark] (iii) Derive the mass conservation equation by starting from the most general form. Clearly under- line and justify each assumption you make. [2 marks] (iv) Derive the momentum equation by starting from the most general form. Clearly underline and justify each assumption you make. (2 marks] (v) Solve for the force to keep the cart moving when Vo = 12 m/s, B = 80 cm and h = 2.5 cm.(1 mark] Vo Scoop Water V Fluid velocity v = 0 Figure 1 Recommended C.V. Water Scoop V V Fluid velocity v = 0 Figure 2

Answer 1

;) lik / - 6 control voliure F o :) This is steady flow, fince, the velocity 앙 surp .is constant. velocity of tuid enter into Therefore, the also is m, the system constant :(VO) "") assume initial mass of the system after then the system then h timedt. travel mass of the system According m₂=m, t would be . to the coursevation of mass : 1 +(PAVO) de A-Bh. Mzim, = P Bh. vodt rate of In gener al form, the changes in mass of the is system ama m-mi с РВЬ yo. dt de

iv) Momentum equatrón: Newton's laws Net Force alting system Rate of change of momenturm т the { Fac = m2 V2 - Vi dt. M₂ Vo -mino de control volume ' that the vo m-mi dt F--(PB hvo.). Vo F.SPBh Vo? feebody diagram. F = P6hvo² the cart with fo force required to more constant Velocity of Vo. V) No= 12 m/s m., hagasycorm 1000x 80x10²x2.5x102 x 12 B: foxiókm., 1 FE PE7880