H6-2 The water volume flow rate through the siphon is 0.005 m3/s, and the pipe diameter is 25 mm. Assume that the flow is frictionless, water is incompressible with a density of 999 kg / m3 , the atmosphere pressure is 101 kPa, and the gravity constant is g = 9.81 m / s" . (a)Determine the velocity of the water in the pipe; (b)If the height h= 4 m, determine the pressure at point A. Answers: (a) 10.2 m/s; (b) 9.83 kPa. H6-3 7.12 from the textbook. Answer: ?? = F / (?VD) = constant. H6-4 To determine the drag on a balloon with a diameter of 1m in a wind speed of 5 m/s (the density of the air is 1.24 kg/m3 and the viscosity of the air is 1.8×10?? N.s/m"), a model with a diameter of 5cm is built for testing in water (the density of the water is 999 kg/m3 and the viscosity of the water is 1×10?3 N.s/m"). What water speed is required to model the prototype? At this speed the model drag is measured to be 2000 N. What will be the corresponding drag on the prototype? Answers: (a) 6.90 m/s; (b) 522 N.
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A venturi meter is used to measure the flow speed of a fluid in a pipe. The meter is connected between two sections of the pipe (Fig. $14-50 ) ;$ the cross-sectional area $A$ of the entrance and exit of the meter matches the pipe's cross-sectional area. Between the entrance and exit, the fluid flows from the pipe with speed $V$ and then through a narrow "throat" of crosssectional area $a$ with speed $v$ . A manometer connects the wider portion of the meter to the narrower portion. The change in the fluid's speed is accompanied by a change $\Delta p$ in the fluid's pressure, which causes a height difference $h$ of the liquid in the two arms of the manometer. (Here $\Delta p$ means pressure in the throat minus pressure in the pipe.) (a) By applying Bernoulli's equation and the equation of continuity to points 1 and 2 in Fig. $14-50$ , show that $$V=\sqrt{\frac{2 a^{2} \Delta p}{\rho\left(a^{2}-A^{2}\right)}}$$ where $\rho$ is the density of the fluid. (b) Suppose that the fluid is fresh water, that the cross-sectional areas are 64 $\mathrm{cm}^{2}$ in the pipe and 32 $\mathrm{cm}^{2}$ in the throat, and that the pressure is 55 $\mathrm{kPa}$ in the pipe and 41 $\mathrm{kPa}$ in the throat. What is the rate of water flow in cubic meters per second?
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