A plate of 1m×1m in size is moving at a constant speed of 5 m/s sideway in a still atmosphere (i.e., its moving direction is parallel to itself). The atmosphere’s kinematic viscosity is 16×10-6 m 2 /s, and density is 1.165kg/m3 . calculate the drag in N.

 Q:- A plate of 1m×1m in size is moving at a constant speed of 5 m/s sideway in a still atmosphere (i.e., its moving direction is parallel to itself). The atmosphere’s kinematic viscosity is 16×10-6 m 2 /s, and density is 1.5 kg/m3 . calculate the drag in N.

ANSWER:- 

Given,

          Area , A = 1x1 = 1 m^2

       Speed , V = 5 m/s^2

kinematic viscosity , v = 0.000016 m^2/sec 

                   Density, ρ = 1.5 kg/m^3

Now,  Reynold's number , Re =  Vl/v = 5x1/0.000016 = 312500

since reynols number is less than 500000 so, flow is laminar.

also , for laminar flow 

coefficient of drag , Cd = 1.328/(Re)^0.5 

                                     

                              Cd  = 1.328/(312500)^0.5 

                                Cd  = 0.002375

So, drag fotrce on both sides of plate is 

                                Fd = 2[ ρAV^2]Cd/2

 

                                Fd = 2[1.5x1x5^2]0.002375/2

                                Fd  = 0.0890625   Newtons

Hence , drag force on the plate is 0.089065N.