Title HPGE 19 Solutions.pdf ✅

19 Hydraulics: Moving Vessel Solutions SITUATION 1. An open rectangular tank mounted on a truck is 5 m long, 2 m wide, and 2.5 m high. It is filled with water to a depth of 2 m. ▣ 1. Compute the smallest amount of an unbalanced force that will cause the greatest force on the rear wall. [SOLUTION] The greatest force on the rear wall will occur when there is water up to the top of the rear wall: tan θ = ax g 1 5 = ax 9.81 m s 2 ax = 1.962 m/s 2 F = ma F = (20 000 kg) (1.962 m s 2 ) F = 39.24 kN ▣ 2. What is the resulting force on the rear wall? [SOLUTION] F = γhA F = (9.81 kN m3 ) ( 2.5 m 2 ) (2.5 m × 2 m) F = 61.3125 kN
▣ 3. What is the resulting force on the bottom of the tank? [SOLUTION] F = γV F = (9.81 kN m3 ) (2 m × 2 m × 5 m) F = 196.2 kN ▣ 4. If the truck accelerated by 2.5 m/s 2 to the right, how much water is spilled? [SOLUTION] tan θ = ax g tan θ = 2.5 9.81 θ = 14.30° y = 5 tan θ = 1.2742 m h = 2.5 m − 1.2742 m h = 1.2258 m Compute for the new volume Vnew = 1 2 (h + 2.5 m)(5 m × 2 m) Vnew = 18.629 m3 Spilled volume: Vspilled = Vold − Vnew Vspilled = 2 m × 2 m × 5 m − 18.629 m3 Vspilled = 1.371 m3 ▣ 5. If the tank moves at a constant speed of 20 m/s, how much water is spilled?