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Chapter 10: Q8P (page 260)
(I) Estimate the pressure needed to raise a column of water to the same height as a 46-m-tall pine tree.
The pressure needed to raise the water column to a height of 46m is 4.50 × 105N/m2.
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(I)How fast does water flow from a hole at the bottom of a very wide, 4.7-m-deep storage tank filled with water? Ignore viscosity.
Will an empty balloon have precisely the same apparent weight on a scale as a balloon filled with air? Explain.
(II)Estimate the air pressure inside a category 5 hurricane, where the wind speed is 300 km/h (Fig. 10-52).
(a) Show that the flow speed measured by a venturi meter (see Fig. 10-29) is given by the relation
\({{\bf{v}}_{\bf{1}}}{\bf{ = }}{{\bf{A}}_{\bf{2}}}\sqrt {\frac{{{\bf{2}}\left( {{{\bf{P}}_{\bf{1}}}{\bf{ - }}{{\bf{P}}_{\bf{2}}}} \right)}}{{{\bf{\rho }}\left( {{\bf{A}}_{\bf{1}}^{\bf{2}}{\bf{ - A}}_{\bf{2}}^{\bf{2}}} \right)}}} \).
(b) A venturi meter is measuring the flow of water; it has a main diameter of \({\bf{3}}{\bf{.5\;cm}}\) tapering down to a throat diameter of \({\bf{1}}{\bf{.0\;cm}}\). If the pressure difference is measured to be \({\bf{18\;mm - Hg}}\), what is the speed of the water entering the venturi throat?
A gardener feels it is taking too long to water a garden with a \(\frac{{\bf{3}}}{{\bf{8}}}\;{\bf{in}}\) diameter hose. By what factor will the time be cut using a \(\frac{{\bf{5}}}{{\bf{8}}}\;{\bf{in}}\) diameter hose instead? Assume nothing else is changed.
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