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Chapter 13: Problem 20

In many problems involving application of Newton's Second Law to the motion of solid objects, friction is neglected for the sake of making the solution easier. The counterpart of friction between solids is viscosity of liquids. Do problems involving fluid flow become simpler if viscosity is neglected? Explain.

Short Answer

Expert verified
Answer: Neglecting viscosity can indeed simplify certain fluid flow problems, such as those involving ideal fluid flow. However, there are cases where considering viscosity is necessary, especially when dealing with boundary layers, turbulence, or other situations where viscous effects play a significant role. Therefore, the decision to neglect viscosity should be made on a case-by-case basis, depending on the problem conditions and the desired level of accuracy.

Step by step solution

01

Understanding Viscosity

Viscosity is a property of fluids that represents their resistance to deformation or flow. It is caused by the internal friction of molecules in the fluid, and it plays a critical role in determining the flow behavior of liquids.
02

Viscosity in Fluid Flow Problems

In problems involving fluid flow, viscosity is often an important factor that determines the behavior of the fluid. For example, in the case of fluid flow through a pipe or between surfaces, the viscous effects can cause the fluid to slow down and create a pressure drop. Additionally, in fluid dynamics problems, viscosity dictates the balance of forces, such as shear stress and pressure gradients.
03

Neglecting Viscosity

In some cases, neglecting viscosity can simplify the problem. For example, in the case of ideal fluid flow, where viscosity is considered negligible, the flow can be assumed to be inviscid and irrotational. This can make the problem easier to solve as it eliminates the need to account for viscous effects in the equations, such as the Navier-Stokes equations.
04

Limitations of Neglecting Viscosity

However, neglecting viscosity can also render some fluid flow problems unrealistic or impossible to solve accurately. For instance, many boundary layer flows and turbulence phenomena are highly influenced by viscous effects, and neglecting them would yield incorrect results. In such situations, considering viscosity is essential to accurately solve the problem.
05

Conclusion

In summary, neglecting viscosity can indeed simplify certain fluid flow problems, such as those involving ideal fluid flow. However, there are cases where considering viscosity is necessary, especially when dealing with boundary layers, turbulence, or other situations where viscous effects play a significant role. Therefore, the decision to neglect viscosity should be made on a case-by-case basis, depending on the problem conditions and the desired level of accuracy.

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Most popular questions from this chapter

A scuba diver must decompress after a deep dive to allow excess nitrogen to exit safely from his bloodstream. The length of time required for decompression depends on the total change in pressure that the diver experienced. Find this total change in pressure for a diver who starts at a depth of \(d=20.0 \mathrm{~m}\) in the ocean (density of seawater \(\left.=1024 \mathrm{~kg} / \mathrm{m}^{3}\right)\) and then travels aboard a small plane (with an unpressurized cabin) that rises to an altitude of \(h=5000 . \mathrm{m}\) above sea level.

Brass weights are used to weigh an aluminum object on an analytical balance. The weighing is done one time in dry air and another time in humid air, with a water vapor pressure of \(P_{\mathrm{h}}=2.00 \cdot 10^{3} \mathrm{~Pa}\). The total atmospheric pressure \(\left(P=1.00 \cdot 10^{5} \mathrm{~Pa}\right)\) and the temperature \(\left(T=20.0^{\circ} \mathrm{C}\right)\) are the same in both cases. What should the mass of the object be to be able to notice a difference in the balance readings, provided the balance's sensitivity is \(m_{0}=0.100 \mathrm{mg}\) ? (The density of aluminum is \(\rho_{\mathrm{A}}=2.70 \cdot 10^{3} \mathrm{~kg} / \mathrm{m}^{3} ;\) the density of brass is \(\left.\rho_{\mathrm{B}}=8.50 \cdot 10^{3} \mathrm{~kg} / \mathrm{m}^{3}\right)\)

A square pool with \(100 .-\mathrm{m}\) -long sides is created in a concrete parking lot. The walls are concrete \(50.0 \mathrm{~cm}\) thick and have a density of \(2.50 \mathrm{~g} / \mathrm{cm}^{3}\). The coefficient of static friction between the walls and the parking lot is \(0.450 .\) What is the maximum possible depth of the pool?

An airplane is moving through the air at a velocity \(v=200 . \mathrm{m} / \mathrm{s} .\) Streamlines just over the top of the wing are compressed to \(80.0 \%\) of their original area, and those under the wing are not compressed at all. a) Determine the velocity of the air just over the wing. b) Find the difference in the pressure between the air just over the wing, \(P\), and that under the wing, \(P\). c) Find the net upward force on both wings due to the pressure difference, if the area of the wing is \(40.0 \mathrm{~m}^{2}\) and the density of the air is \(1.30 \mathrm{~kg} / \mathrm{m}^{3}\).

Blood pressure is usually reported in millimeters of mercury (mmHg) or the height of a column of mercury producing the same pressure value. Typical values for an adult human are \(130 / 80\); the first value is the systolic pressure, during the contraction of the ventricles of the heart, and the second is the diastolic pressure, during the contraction of the auricles of the heart. The head of an adult male giraffe is \(6.0 \mathrm{~m}\) above the ground; the giraffe's heart is \(2.0 \mathrm{~m}\) above the ground. What is the minimum systolic pressure (in \(\mathrm{mmHg}\) ) required at the heart to drive blood to the head (neglect the additional pressure required to overcome the effects of viscosity)? The density of giraffe blood is \(1.00 \mathrm{~g} / \mathrm{cm}^{3},\) and that of mercury is \(13.6 \mathrm{~g} / \mathrm{cm}^{3}\)
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