As the hydraulic cylinder rotates around O, the ex- posed length l of the piston rod P is controlled by the action of oil pressure in the cylinder. If the cylinder rotates at the constant rate 0 = 60 deg/s and l is decreasing at the constant rate of 150 mm/s, calculate the magnitudes of the velocity v %3D and acceleration a of end B when I 125 mm. %3D

6 Consider a fully developed laminar flow of a fluid through 8027 m long and 4 cm diameter horizontal and circular pipe. The dynamic density and the viscosity of the fluid are 1252 kg/m³ and 0.3073 kg/(m.s). The velocity profile at a cross-section is given by: u(r)= 6[1 − ( 7 )²] - m/s Where r is the axial distance from the centre and R is the radius of the pipe. Determine the following: (i) (ii) the maximum velocity at a cross-section of the pipe, Umax the average velocity at a cross-section of the pipe, Vave the volume flow rate, Q (iv) Reynolds number, Re (v) friction factor, f (vi) head loss, hi (vii) pressure loss, AP (viii) pumping power required, (ix) for the same pumping power, the percentage decrease of the flow rate if the pipe is inclined 10° upward (assume the head loss, hò, calculated in part (vi) does not change) Useful formulae: 64 f Re h₂ = f ( =) ( 2² ) 2g =

Ex. A pitot static probe is inserted into duct of air heating system parall to flow and the differential height of the water Colum is measured. The flow velocity and the pressure rise at the of the pitot -statics probe are to be determined For water p = 1000 kg/m3. for air p = 1.1 kg/m3 Air h-2.4 cm

6/97 The 1.2-kg uniform slender bar rotates freely about a horizontal axis through O. The system is released from rest when it is in the horizontal position 0-0, where the spring is unstretched. If the bar is observed to momentarily stop in the position 0-50°, determine the spring constant k. For your computed value of k, what is the angular velocity of the bar when 0 -25°? B 0.6 m 0.6 m A 0.2 m 1.2 kg