Question

QUESTION 2A (11 marks) [Allow 13 minutes] Water flows over a stationary, smooth, flat rectangular plate with dimensions 0.4 x 0.25m as shown in the figure below. The plate has its long axis parallel to the direction of flow 0.4 m U1 m/s 0.25 m Answer the questions below where the properties of the water are (p 1000 kg/m, v 106 m2/s): a) Determine the nature of the boundary layer over the plate if the approach velocity of the water, Uo1 m/s. [2 marks] b) Determine the thickness of the boundary layer at the trailing edge of the plate. 2 marks] c) Find the shear force, Fr on the plate taking into account skin drag on both sides [3 marks] d) If the approach flow velocity was increased to 5 m/s, explain what would [2 marks] happen to the boundary layer over the plate. e) If the plate was rotated through 90 degrees such that the long axis is perpendicular to the flow, will the shear force on the two plates be the same or different? Briefly give your reasoning. [2 marks]

Answer 1

Answer:

first we must determine the Reynold's number

a) Reynold's number = Re = U0 * L / $\nu$

= 1*0.4 / 10^(-6)

= 250000

= 4*10^5 which is < 5* 10^5

thus flow is laminar, so BL is laminar

b) BL thickness = $\delta$ = 5*x / sqrt(Re)

= 5* 0.4 / sqrt(4*10^5)

= 3.16* 10^-3 m

c) Coefficient of drag = Cd = 1.328 / sqrt(Re)

= 1.328 / sqrt( 4*10^5)

= 2.1*10^-3

drag Force = Df = 2* Cd *0.5* area * density *U0^2

( multiplied by 2 as both sides)

= 2* 2.1*10^-3 * 0.5 * 0.25*0.4 * 1000 * 1^2

= 0.2099 N

If approach velocity = U0 = 5m/s

then Re will be increased 5 times

= 4*5 * 10^5

= 20* 10^5

thus it will become a turbulent BL