Question

1. A very smooth flat plate of length L = 0.5 m and width b = 2 m is immersed parallel to a stream of velocity 2 m/s. For both air and water as the working fluids; a. Show that the flow is completely laminar over the entire plate. (5 marks] b. Determine the drag force on one side of the plate. [4 marks] c. Determine the thicknesses , 8*, and at the end of the plate (x = L). (6 marks] For air use, p = 1.23 kg/m and y = 1.46 x 105 m/s For water use p = 1000 kg/m and v = 1.02 x 10 mm/s. A general rule of thumb is that the transition to turbulence occurs for the flow over a smooth flat plate occurs at a transition-to-turbulence Reynolds number of Rex.tr = 5 x 10°. This plate is very very smooth, so for this question we will assume a transition-to-turbulence Reynolds number of Rex.tr = 3 x 10

Answer 1

L=0.5m 6= 2m v= 2 m/s critical Reynolds no Rexto Reg= 3x106 - For air P = 1,23 kg/m 2 = 1.46 x 100 ml a) for flow to be laminar Re<Reer At the end of plate Re-Sul = ve u v = 2x0.5 = 0.684x10S <3x100 1.46x155 So, the flow is completely laminar, 6) drag force drag coefficient for entire plate Co = 1.328 ✓re Re = 0.684x108 - 6=0.005077 drag force - I CGPA v² = 1 (0.00 5077) (1.23) (0.5x2) (2) ² 10.0124N c) Boundary layer thickness (at end of plate) s = 5x = 5x0.5 = 0.00955 m Rexlxol Jo. 684x105 s = 9.558 mm

Taking velouty profile in laminar flow to be- Then displacement thickness Us 0 g* = 25 - x 9.558 5* = 6.372 mm momentum thickness Oul-udy - S = 28 5 15 25 382 557To og = 2 x 9.558 = 2 x 15 9.558 o=1. 274 mm

- for water 8=1000kg = 1,02x10 t mic a) At the end of plate - vl = 2x0.5 = 0.98x106 <3x100 0 1 .02x10-6 So, the flow is completely laminar 6 1,350 1. drag force drag wefficient Co- 1.328 = 1.328 Co = 0.00134 drag force - Co s Av 1 (0.00134) (1000) (2x0.5) (2) - =2.6820 c) Boundary layer thickness &= 5x1 = 5x05 Rex lx= √0.98x106 = 0.00252 S=2.524 mm displacement thickness = 28 = 2x2.524 1 * = 1.683 mm

Momentum thickness olue. 1-Cos) ay - (+)ey = 28 = 2 x 2.524 15 15 0 - 0.3366 mm