8. [2 points] Consider a tank, with circular cross-section of diameter (D.). The tank contains water and is open to atmosphere. A cylindrical pipe with circular cross section and diameter (D) is connected at the bottom of the tank and is open to the atmosphere. At t=0 (which is the instant shown in figure), the height of the water column is (h). Assume that D₁ >> D, and the flow is quasi-steady. The length of the pipe is L, and water density and dynamic viscosity are p and μ, respectively. The tank and pipe are open to atmosphere and losses within the tank are negligible. For the instant shown, and indicating all detailed steps, (a) [0.5 point] Find the gage pressure (Pa) at the entrance to the pipe (point 'a'), if all losses are negligible. (b) [1 point] Find an expression for the the gage pressure at point 'a', if only major losses inside the pipe based on the friction factor f are considered. Assume f is known. (c) [0.5 point] Will the gage pressure in part (b) higher, smaller, or same as compared to that in part (a)? Diameter D gage Pa (without losses) = gage Pa (with losses) = compare gage Pa (with and without losses) =

Fig: 1