By Frank M. White
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Solution: The following notes are from Rouse and Ince [Ref. 23]. Hagen (1884) was born in Königsberg, East Prussia, and studied there, having among his teachers the famous mathematician Bessel. He became an engineer, teacher, and writer and published a handbook on hydraulic engineering in 1841. 5 to 6 mm, and lengths of 47 to 110 cm. The measurements indicated that the pressure drop was proportional to Q at low heads and proportional (approximately) to Q2 at higher heads, where “strong movements” occurred—turbulence.
Assume that the atmosphere offers no shear resistance to the film surface. (a) Sketch the approximate shape of the velocity profile w(x), keeping in mind the boundary conditions. Ans. (b) Chapter 1 • Introduction 57 (b) Suppose film thickness d is measured, along with the slope of the velocity profile at the wall, (dw/dx)wall, with a laser-Doppler anemometer (Chap. 6). Find an expression for µ as a function of ρ, δ, (dw/dx)wall, and g. Note that both w and (dw/dx)wall will be negative as shown.
2 m) Solve for the pressure in the air space: pair ≈ 10500 Pa Ans. 11 In Fig. 5 kPa (gage). All fluids are at 20°C. Determine the elevations Z in meters of the liquid levels in the open piezometer tubes B and C. Solution: (B) Let piezometer tube B be an arbitrary distance H above the gasolineglycerin interface. 0 N/m3, γgasoline = 6670 N/m3, and γglycerin = 12360 N/m3. Then apply the hydrostatic formula from point A to point B: Fig. 73 m (23 cm above the gasoline-air interface) Ans. (b) Solution (C): Let piezometer tube C be an arbitrary distance Y above the bottom.