6. A mercury manometer (p = 13,600 kg/m) is connected to an air duct to measure the pressure inside. The difference in the manometer levels is 15 mm, and the atmospheric pressure is 100 kPa. (a) Judging from the figure, determine Air A15 mm if the pressure in the duct is above or below the atmospheric pressure. (b) Determine the absolute pressure in the duct.

Navier-Stokes, Cylindrical. Water flows in a vertical pipe of radius R = 2 cm. In the coordinates shown: (a) solve for V(r) in terms of dp/dz, μ, R, p, and g. (b) evaluate the flow rate down the pipe if dp/dz = 0; (c) evaluate the minimum value of dp/dz needed to stop the flow from going down the pipe?; (d) what value of dp/dz is required to have the flow go up the pipe at the same as the flow rate down in part 'b' ? ; (e) what is the centerline (r = 0) speed for each of the conditions (i.e. dp/dz) in each of b,c,d? Units for expecting: (a) Vz = C1 [r^2/R^2 - 1]; (b) Q: 10^-1 m^3 /s; (c) dp/dz,stop: 10^3 Pa/m; (d) dp/dz,up: 10^4 Pa/m; (e) Vb = 10^2 m/s; Vc = 10^0 m/s ; Vd = -10^2 m/s SI constant Patm = 10^5 Pa; pwater ~ 1000 kg/m^3; pair - 1.2kg/m^3; μwater - 10^-3 N•s/m^2; pair ~ 2 x 10^-5 N•s/m^2; g = 9.8 m/s^2 R Aft

A pair of concentric glass cylinders, with diameters of 1 and 1.05 cm, respectively are held together in such a way that both annular ends are open to the flow of fluids. The pair of cylinders with its axis vertical are so placed that the open end is slightly below the surface of a reservoir of silicone oil at 25 deg. C. What is the expected height of the oil into the annular space between the cylinders? Take o=0.019 N/m and p=900 kg/m³.

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