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Chapter 8: Problem 5

What fluid property is responsible for the development of the velocity boundary layer? For what kinds of fluids will there be no velocity boundary layer in a pipe?

Short Answer

Expert verified
Answer: The fluid property responsible for the development of the velocity boundary layer is viscosity. The type of fluids that will not result in a velocity boundary layer are ideal or inviscid fluids, which have zero viscosity. However, these fluids are theoretical constructs and do not exist in reality.

Step by step solution

01

Identify the fluid property responsible for the development of the velocity boundary layer

The fluid property responsible for the development of the velocity boundary layer is viscosity. Viscosity is the measure of a fluid's resistance to flow and causes the fluid to stick to the walls of the pipe or any solid surface, leading to the development of the velocity boundary layer.
02

Determine the type of fluids without a velocity boundary layer

For a fluid to have no velocity boundary layer, its viscosity must be zero. Such fluids are called ideal or inviscid fluids, which have the property that their viscosity is equal to zero, and they do not form a boundary layer when flowing through a pipe. However, it's important to note that ideal fluids are theoretical constructs and do not exist in reality. All real fluids have some viscosity and will develop a boundary layer.

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Most popular questions from this chapter

Air ( \(1 \mathrm{~atm})\) enters into a 5 -cm-diameter circular tube at \(20^{\circ} \mathrm{C}\) with an average velocity of \(5 \mathrm{~m} / \mathrm{s}\). The tube wall is maintained at a constant surface temperature of \(160^{\circ} \mathrm{C}\), and the outlet mean temperature is \(80^{\circ} \mathrm{C}\). Estimate the length of the tube.

In a thermal system, water enters a \(25-\mathrm{mm}\)-diameter and \(23-\mathrm{m}\)-long circular tube with a mass flow rate of \(0.1 \mathrm{~kg} / \mathrm{s}\) at \(25^{\circ} \mathrm{C}\). The heat transfer from the tube surface to the water can be expressed in terms of heat flux as \(\dot{q}_{s}(x)=a x\). The coefficient \(a\) is \(400 \mathrm{~W} / \mathrm{m}^{3}\), and the axial distance from the tube inlet is \(x\) measured in meters. Determine \((a)\) an expression for the mean temperature \(T_{m}(x)\) of the water, \((b)\) the outlet mean temperature of the water, and \((c)\) the value of a uniform heat flux \(\dot{q}_{s}\) on the tube surface that would result in the same outlet mean temperature calculated in part (b). Evaluate water properties at \(35^{\circ} \mathrm{C}\).

Air \(\left(c_{p}=1000 \mathrm{~J} / \mathrm{kg} \cdot \mathrm{K}\right)\) enters a 20 -cm-diameter and 19-m-long underwater duct at \(50^{\circ} \mathrm{C}\) and \(1 \mathrm{~atm}\) at an average velocity of \(7 \mathrm{~m} / \mathrm{s}\) and is cooled by the water outside. If the average heat transfer coefficient is \(35 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\) and the tube temperature is nearly equal to the water temperature of \(5{ }^{\circ} \mathrm{C}\), the exit temperature of air is (a) \(8^{\circ} \mathrm{C}\) (b) \(13^{\circ} \mathrm{C}\) (c) \(18^{\circ} \mathrm{C}\) (d) \(28^{\circ} \mathrm{C}\) (e) \(37^{\circ} \mathrm{C}\)

Hot water at \(90^{\circ} \mathrm{C}\) enters a \(15-\mathrm{m}\) section of a cast iron pipe \((k=52 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K})\) whose inner and outer diameters are 4 and \(4.6 \mathrm{~cm}\), respectively, at an average velocity of \(1.2 \mathrm{~m} / \mathrm{s}\). The outer surface of the pipe, whose emissivity is \(0.7\), is exposed to the cold air at \(10^{\circ} \mathrm{C}\) in a basement, with a convection heat transfer coefficient of \(12 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\). Taking the walls of the basement to be at \(10^{\circ} \mathrm{C}\) also, determine \((a)\) the rate of heat loss from the water and \((b)\) the temperature at which the water leaves the basement.

In fully developed laminar flow inside a circular pipe, the velocities at \(r=0.5 R\) (midway between the wall surface and the centerline) are measured to be 3,6 , and \(9 \mathrm{~m} / \mathrm{s}\). (a) Determine the maximum velocity for each of the measured midway velocities. (b) By varying \(r / R\) for \(-1 \leq\) \(r / R \leq 1\), plot the velocity profile for each of the measured midway velocities with \(r / R\) as the \(y\)-axis and \(V(r / R)\) as the \(x\)-axis.
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