Chapter 2: Problem 42
Explain how an ice skate interacts with the ice surface. What mechanism acts to reduce sliding friction between skate and ice?
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Chapter 2: Problem 42
Explain how an ice skate interacts with the ice surface. What mechanism acts to reduce sliding friction between skate and ice?
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The velocity for a steady, incompressible flow in the \(x y\) plane is given by \(\vec{V}=i A / x+i A y / x^{2},\) where \(A=2 \mathrm{m}^{2} / \mathrm{s},\) and the coordinates are measured in meters. Obtain an equation for the streamline that passes through the point \((x, y)=\) (1,3). Calculate the time required for a fluid particle to move from \(x=1 \mathrm{m}\) to \(x=2 \mathrm{m}\) in this flow field.
The variation with temperature of the viscosity of air is correlated well by the empirical Sutherland equation \\[\mu=\frac{b T^{1 / 2}}{1+S / T}\\] Best-fit values of \(b\) and \(S\) are given in Appendix A for use with SI units. Use these values to develop an equation for calculating air viscosity in British Gravitational units as a function of absolute temperature in degrees Rankine. Check your result using data from Appendix A.
A viscous clutch is to be made from a pair of closely spaced parallel disks enclosing a thin layer of viscous liquid. Develop algebraic expressions for the torque and the power transmitted by the disk pair, in terms of liquid viscosity, \(\mu\) disk radius, \(R,\) disk spacing, \(a,\) and the angular speeds: \(\omega_{i}\) of the input disk and \(\omega_{o}\) of the output disk. Also develop expressions for the slip ratio, \(s=\Delta \omega / \omega_{i},\) in terms of \(\omega_{i}\) and the torque transmitted. Determine the efficiency, \(\eta,\) in terms of the slip ratio.
An insulation company is examining a new material for extruding into cavities. The experimental data is given below for the speed \(U\) of the upper plate, which is separated from a fixed lower plate by a 1 -mm-thick sample of the material, when a given shear stress is applied. Determine the type of material. If a replacement material with a minimum yield stress of \(250 \mathrm{Pa}\) is needed, what viscosity will the material need to have the same behavior as the current material at a shear stress of \(450 \mathrm{Pa} ?\) $$\begin{array}{ccccccccccc}\tau(P a) & 50 & 100 & 150 & 163 & 171 & 170 & 202 & 246 & 349 & 444 \\ U(\mathrm{m} / \mathrm{s}) & 0 & 0 & 0 & 0.005 & 0.01 & 0.025 & 0.05 & 0.1 & 0.2 & 0.3 \end{array}$$
A shaft with outside diameter of \(18 \mathrm{mm}\) turns at 20 revolutions per second inside a stationary journal bearing \(60 \mathrm{mm}\) long. A thin film of oil \(0.2 \mathrm{mm}\) thick fills the concentric annulus between the shaft and journal. The torque needed to turn the shaft is \(0.0036 \mathrm{N} \cdot \mathrm{m}\). Estimate the viscosity of the oil that fills the gap.
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