The viscosity, n, of a fluid used in the production environment is defined by the equation F d where F is the force acting over an area A, and v1, v2 are the velocities at two points a distance d apart in the fluid. (a) Apply dimensional analysis to determine the dimensions of viscosity using the given equation. (b) When a sphere of radius a and density p falls through a fluid with viscosity n, it reaches a terminal velocity v given by: 2a2pg 97 Apply dimensional analysis to show that this formula is dimensionally homogeneous. (c) The Reynolds number, R, for the flow of fluid round an obstruction of width w is a dimensionless quantity given by: R = pwn where v is the velocity of the flow, r is the density of the fluid and in its viscosity. Use dimensional analysis, to obtain the values of a, and y. (d) The design team is investigating the flow of air round an aircraft of width, X moving with velocity 150, at a height where the air has density 0.4 and viscosity 1.6 x 10-5 (all in SI units). A prototype of the aircraft, with width Y, is used in a wind tunnel at ground level, where the air has density 1.3 and viscosity 1.8 x 105. The Reynolds number for the prototype must be the same as that for the full-sized aircraft. Use dimensional analysis to find the velocity of flow required in the wind tunnel.