(Solved): Q1-) a-) Consider fully developed laminar flow in a circular pipe. If the diameter of the pipe is r ...

Q1-) a-) Consider fully developed laminar flow in a circular pipe. If the diameter of the pipe is reduced by half while the volume flow rate, $\mathrm{Q}$, and the pipe length, $\mathrm{L}$ are held constant, the head loss, ${\mathrm{h}}_{\mathrm{f}}$ will (a) double, (b) triple, (c) quadruple, (d) increase by a factor of 8 , or (e) increase by a factor of 16 . Please find the correct answer by using the following equations; $\mathrm{U}=\mathrm{Q}/\mathrm{A};\mathrm{Re}=(?\mathrm{UD})/?$ and ${\mathrm{h}}_{\mathrm{f}}=\frac{64}{\mathrm{Re}}\frac{\mathrm{L}}{\mathrm{D}}\frac{{\mathrm{u}}^2}{2\mathrm{g}}$ b-) We know that the lift coefficient, ${\mathrm{C}}_{\mathrm{L}}$ of the wing without flaps is equal to 1.52 . When the wing is coupled with the flap the lift coefficient, ${\mathrm{C}}_L$ of the wing increase to a value of 2.67 by having a slot between the wing and the flap as seen in the figure. Why do you think the lift coefficient, $C_L$ increases? Please explain properly. c-) Explain under which conditions the static pressure changes non-linearly along the straight pipe of an incompressible, steady and turbulent flow. b-2) Prove that the velocity increases in the converging part of the nozzle and decreases in the divergent part of the nozzle using the following equation. $\frac{dA}{A}=?\frac{dV}{V}\left(1?{\mathrm{Ma}}^2\right)$