Question

Need help with this Fluid Mechanics question. Please help me to solve step by step. Thank you!

Initial mass, Mo 4.27 A pressurized tank of water is mounted on a cart as shown. A jet issues from a nozzle in the tank at a constant speed and propels the cart along a horizontal track. The initial mass of the cart and tank is 100 kg, and the nozzle area is 0.005 m2. Determine the jet speed required to accelerate the cart to 1.5 m/s in 30 s. U V A

Answer 1

From Equation of continuity dM Mrate & Constant dt Mratet M.-(PAV) + M= M. - Momentum Equation in n-direction, - aM = – SV²A a - du dt du (M. JA VE) = -8V²A dt at du - SV²A M. -SAVt 4 Integrating t Jau du - t 0 SUZA & (M. - SAVE) sv’A (- ln(M16 - PAVE) PAVE) SAV u. t u » V- Jet speed u V en (Mo - SA vt] u v[en (M.) In (M. - Savt)] M M J SAVE substituting values 1.5 100 - 999% 0.005 V X 30 we get -0.6102 m/s en V So wing in

2 -2 0 2 -2 f(x) = 1.5 X 100 100 - 149.85X

III 0:00005 0.6101 0.6102 0.6 -0:00005 f(x) = 1,5 - Ir 100 100 – 149.85x