P7.16 A thin flat plate 55 by 110 cm is immersed in a 6-m/s stream of SAE 10 oil at 20C. Compute the total friction drag if the stream is parallel to (a) the long side and (b) the short side.

a

The total friction drag for the long side of the plate is 107 N

b

The total friction drag for the long side of the plate is 151.4 N

Explanation:

The first question is to obtain the friction drag when the fluid i parallel to the long side of the plate

The block representation of the this problem is shown on the first uploaded image  

Where the U is the initial velocity = 6 m/s

    So the equation we will be working with is

    Where is the density of SAE 10W = This is obtained from the table of density at 20° C

                is the friction drag coefficient

   This coefficient is dependent on the Reynolds number if the Reynolds number is less than then the flow is of laminar type and

           =

But if the Reynolds number is greater than the flow would be of Turbulent type and

Where Re is the Reynolds number

   To obtain the  Reynolds number  

          where L is the length of the long side = 110 cm = 1.1 m

 and is the Dynamic viscosity of SAE 10W oil

  This is gotten from the table of Dynamic viscosity of oil

  So        

Since            55211.54 <

Hence

                  is the area of the plate  = =

Since the area is immersed totally it should be multiplied by 2 i.e the bottom face and the top face are both immersed in the fluid

Considering the short side

            To obtain the Reynolds number

Here b is the short side

Since the value obtained is not greater than then the flow is laminar

   And

The next thing to do is to obtain the total friction drag

      Substituting values

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a straight line sloped