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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

An approximately round tendon that has an average diameter of \(8.5 \mathrm{~mm}\) and is \(15 \mathrm{~cm}\) long is found to stretch \(3.7 \mathrm{~mm}\) when acted on by a force of \(13.4 \mathrm{~N}\). Calculate Young's modulus for the tendon.

Water of density \(998.2 \mathrm{~kg} / \mathrm{m}^{3}\) is moving at negligible speed under a pressure of \(101.3 \mathrm{kPa}\) but is then accelerated to high speed by the blades of a spinning propeller. The vapor pressure of the water at the initial temperature of \(20.0^{\circ} \mathrm{C}\) is \(2.3388 \mathrm{kPa}\). At what flow speed will the water begin to boil? This effect, known as cavitation, limits the performance of propellers in water

You fill a tall glass with ice and then add water to the level of the glass's rim, so some fraction of the ice floats above the rim. When the ice melts, what happens to the water level? (Neglect evaporation, and assume that the ice and water remain at \(0^{\circ} \mathrm{C}\) during the melting process.) a) The water overflows the rim. b) The water level drops below the rim. c) The water level stays at the top of the rim. d) It depends on the difference in density between water and ice.

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 \(13.6 \mathrm{~g} / \mathrm{cm}^{3}\)

An open-topped tank completely filled with water has a release valve near its bottom. The valve is \(1.0 \mathrm{~m}\) below the water surface. Water is released from the valve to power a turbine, which generates electricity. The area of the top of the tank, \(A_{\mathrm{p}}\) is 10 times the cross-sectional area, \(A_{\mathrm{y}}\) of the valve opening. Calculate the speed of the water as it exits the valve. Neglect friction and viscosity, In addition, calculate the speed of a drop of water released from rest at \(h=1.0 \mathrm{~m}\) when it reaches the elevation of the valve, Compare the two speeds.
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