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Chapter 3: Problem 30
Water flows through a hole in the bottom of a large, open tank with a speed of \(8 \mathrm{m} / \mathrm{s}\), Determine the depth of water in the tank. Viscous effects are negligible.
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Observations show that it is not possible to blow the table tennis ball from the funnel shown in Fig. \(\mathrm{P} 3.122 a\). In fact, the ball can be kept in an inverted funnel, Fig. \(P 3.122 b,\) by blowing though it. The harder one blows through the funnel, the harder the ball is held within the funnel. Try this experiment on your own. Explain this phenomenon.
The Bemoulli equation is valid for steady, inviscid, incompressible flows with constant acceleration of gravity. Consider flow on a planet where the acceleration of gravity varies with height so that \(g=g_{0}-c z,\) where \(g_{0}\) and \(c\) are constants. Integrate \(" \mathbf{F}=m \mathbf{a}^{\prime \prime}\) along a streamline to obtain the equivalent of the Bernoulli equation for this flow.
Water flows in a vertical pipe of 0.15 -m diameter at a rate of \(0.2 \mathrm{m}^{3} / \mathrm{s}\) and a pressure of \(200 \mathrm{kPa}\) at an elevation of \(25 \mathrm{m}\). Determine the velocity head and pressure head at elevations of 20 end 55 m.
A 40 -mph wind blowing past your house speeds up as it flows up and over the roof. If elevation effects are negligible, determine (a) the pressure at the point on the roof where the speed is 60 mph if the pressure in the free stream blowing toward your house is 14.7 psia. Would this effect tend to push the roof down against the house, or would it tend to lift the roof? (b) Determine the pressure on a window facing the wind if the window is assumed to be a stagnation point.
Figure \(P 3.119\) shows two tall towers. Air at \(10^{\circ} \mathrm{C}\) is blowing toward the two towers at \(V_{0}=30 \mathrm{km} / \mathrm{hr}\). If the two towers are \(10 \mathrm{m}\) apart and half the air flow approaching the two towers passes between them, find the minimum air pressure between the two towers. Assume constant air density, inviscid flow, and steady-state conditions. The atmospheric pressure is \(101 \mathrm{kPa}\).
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