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Chapter 10: Q18P (page 260)

Water and then oil (which don鈥檛 mix) are poured into a U-shaped tube, open at both ends. They come to equilibrium as shown in Fig. 10鈥�50. What is the density of the oil? [Hint: Pressures at points a and b are equal. Why?]

Short Answer

Expert verified

The density of oil is 683 kg/m3.

Step by step solution

01

Understanding the effective pressure

The effective pressure of a fluid is equivalent to the product of density, depth of the fluid, and acceleration due to gravity. The effective pressure at points at the same height will be identical.

02

Given the data

The height of the oil column above a is H = 27.2cm.

The height of the air column above point b is h =8.62cm.

03

Calculation of density of oil


The effective pressure at points a and b will be the same as they are at the same height. The density of water is 蟻w = 1000kg/m. Assume the density of oil is 蟻oand the atmospheric pressure is P.

The relation of pressure at points a and b is given by,

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Most popular questions from this chapter

Two ships moving in parallel paths close to one another risk colliding. Why?

Four lawn sprinkler heads are fed by a 1.9-cm-diameter pipe. The water comes out of the heads at an angle of 35掳 above the horizontal and covers a radius of 6.0 m. (a) What is the velocity of the water coming out of each sprinkler head? (Assume zero air resistance.) (b) If the output diameter of each head is 3.0 mm, how many liters of water do the four heads deliver per second? (c) How fast is the water flowing inside the 1.9-cm-diameter pipe?

(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?

Why does the stream of water from a faucet become narrower as it falls (Fig. 10鈥�43)?

FIGURE 10鈥�43 Question 12. Water coming from a faucet.

How high should the pressure head be if water is to come from a faucet at a speed of \({\bf{9}}{\bf{.2\;m/}}{{\bf{s}}^{\bf{2}}}\) Ignore viscosity.
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