Azzle at a velo- on ure P7.1 city diameter 5 i ontal reaction luc stic atio...

Transcribed Image Text:

Azzle at a velo- on ure P7.1 city diameter 5 i ontal reaction luc stic atio Vate n re that turned the flow 45%, respectively. What happens when the plate is parallel to the flow? Consider the geometry shown in Fig. ure P7.18. The fluid approaches the leading edge of the plate with a uniform velocity u = Ugi. The no-slip condition at the plate surface forces the fluid velocity to zero at y= 0. The slowly moving fluid particles near the surface exert a drag on the adjacent fluid molecules such that a roughly parabolic velocity profile develops in the boundary layer. At any distance y from the leading edge of the plate, the boundary layer has a characteristic thickness 8. The velocity pro- file at a specific value of x is given by u = Uul2(y/8)-(y/812]i. In this particular problem the fluid is air with a density of 1.22 kg/m, Up = 140 km/h, the x coordinate has been selected such that 8=1 cm, and the plate has a width of 1.3 m. (a) Calculate the volume flowrate of air through the top surface of the indicated control volume. (b) Calculate the drag force on the plate in the x direction. 7.45 es Shown in Figure I g 7.48 R d er th Wa U 45 Figure P7.17 7.47 Problems P7.45 and P7.46 dealt with a prate at 90 to the flow and an angled plate Up Figure P7.18 Up CS 8 = 1 cm SU Azzle at a velo- on ure P7.1 city diameter 5 i ontal reaction luc stic atio Vate n re that turned the flow 45%, respectively. What happens when the plate is parallel to the flow? Consider the geometry shown in Fig. ure P7.18. The fluid approaches the leading edge of the plate with a uniform velocity u = Ugi. The no-slip condition at the plate surface forces the fluid velocity to zero at y= 0. The slowly moving fluid particles near the surface exert a drag on the adjacent fluid molecules such that a roughly parabolic velocity profile develops in the boundary layer. At any distance y from the leading edge of the plate, the boundary layer has a characteristic thickness 8. The velocity pro- file at a specific value of x is given by u = Uul2(y/8)-(y/812]i. In this particular problem the fluid is air with a density of 1.22 kg/m, Up = 140 km/h, the x coordinate has been selected such that 8=1 cm, and the plate has a width of 1.3 m. (a) Calculate the volume flowrate of air through the top surface of the indicated control volume. (b) Calculate the drag force on the plate in the x direction. 7.45 es Shown in Figure I g 7.48 R d er th Wa U 45 Figure P7.17 7.47 Problems P7.45 and P7.46 dealt with a prate at 90 to the flow and an angled plate Up Figure P7.18 Up CS 8 = 1 cm SU