Question

Fluid Mechanics

5. (20 points) A horizontal conveyor belt moving at 3 m/s receives sand from a container. The sand falls vertically from the container to the belt at a speed of 1.5 m/s and a flow rate of 200 kg/s. The conveyor belt is initially empty but begins to fill with sand. If the friction in the drive system and rollers is negligible. find the force required to pull the belt while the conveyor is filling. sand 60° у V = 1.5 m/s sand V. = 3 m/s x

Fluid Mechanics

Answer 1

60" N=1.5m/s Now, Resolving the Velocity vector(s) Vscoso ?b=20m/s 200kgls Vg V Sino $1603 Tavscose Ta= 1.5 Cosbol 1.5 = 0.75m/s direction of Va&lb is some So total velocity for Sond= TatVb av = 3.75m/s 0.75 +3

Gliven mass=200kg = 5 Sec F = N = Kam force, F = mx V = 200kg x 3-4son's elu Sec S Axulu = = 750 kyn S² f = 75ON
first of all we have resolve the Vs into horizontal and vertical components. The horizontal component is cos theta component and theta is 60degree here. This component is in direction of vb so for total velocity both velocity is added and then force is calculated.