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Chapter 10: Q23P (page 260)

(II) What fraction of iron will be submerged when it floats in mercury?

Short Answer

Expert verified

The fraction of iron in mercury is 0.57.

Step by step solution

01

Understanding the floatation of a solid

For equilibrium, during floatation, the weight of the substance will be equal to the buoyant force of the fluid.

02

Calculation the fraction of the iron

The buoyant force due to the Vin part of the iron inside mercury is,

FB = Vinρg

Here, ρf = 13.6 x 103 kg/m3 is the density of the mercury, and g is the gravitational acceleration.

The weight of iron of volume V is,

W = Vρsg

Here, ρs = 7.8 x 103 Kg/m3 is the density of the iron.

Equate these two forces for equilibrium and get,

Substitute the given values and get,

Hence, the submerged fraction of iron is 0.57.

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Most popular questions from this chapter

(I) Engine oil (assume SAE 10, Table 10–3) passes through a fine \({\bf{1}}{\bf{.80}}\;{\bf{mm}}\)-diameter tube that is \({\bf{10}}{\bf{.2}}\;{\bf{cm}}\)long. What pressure difference is needed to maintain a flow rate of \({\bf{6}}{\bf{.2}}\;{\bf{mL/min}}\)?

In Fig. 10-54, take into account the speed of the top surface of the tank and show that the speed of fluid leaving an opening near the bottom is \({{\bf{v}}_{\bf{1}}}{\bf{ = }}\sqrt {\frac{{{\bf{2gh}}}}{{\left( {{\bf{1 - A}}_{\bf{1}}^{\bf{2}}{\bf{/A}}_{\bf{2}}^{\bf{2}}} \right)}}} \),

where \({\bf{h = }}{{\bf{y}}_{\bf{2}}} - {{\bf{y}}_{\bf{1}}}\), and \({{\bf{A}}_{\bf{1}}}\) and \({{\bf{A}}_{\bf{2}}}\) are the areas of the opening and of the top surface, respectively. Assume \({{\bf{A}}_{\bf{1}}}{\bf{ < < }}{{\bf{A}}_{\bf{2}}}\) so that the flow remains nearly steady and laminar.

Figure 10-54

(II) Poiseuille’s equation does not hold if the flow velocity is high enough that turbulence sets in. The onset of turbulence occurs when the Reynolds number, \(Re\) , exceeds approximately 2000. \(Re\) is defined as

\({\mathop{\rm Re}\nolimits} = \frac{{2\overline v r\rho }}{\eta }\)

where \(\overline v \) is the average speed of the fluid, \(\rho \) is its density, \(\eta \) is its viscosity, and \(r\) is the radius of the tube in which the fluid is flowing. (a) Determine if blood flow through the aorta is laminar or turbulent when the average speed of blood in the aorta \(\left( {{\bf{r = 0}}{\bf{.80}}\;{\bf{cm}}} \right)\) during the resting part of the heart’s cycle is about \({\bf{35}}\;{\bf{cm/s}}\). (b) During exercise, the blood-flow speed approximately doubles. Calculate the Reynolds number in this case, and determine if the flow is laminar or turbulent.

Question: A hydraulic lift is used to jack a 960-kg car 42 cm off the floor. The diameter of the output piston is 18 cm, and the input force is 380 N. (a) What is the area of the input piston? (b) What is the work done in lifting the car 42 cm? (c) If the input piston moves 13 cm in each stroke, how high does the car move up for each stroke? (d) How many strokes are required to jack the car up 42 cm? (e) Show that energy is conserved.

A small amount of water is boiled in a 1-gallon metal can. The can is removed from the heat and the lid is put on. As the can cool, it collapses and looks crushed. Explain.
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