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In any forced or natural convection situation, the velocity of the flowing fluid is zero where the fluid wets any stationary surface. The magnitude of heat flux where the fluid wets a stationary surface is given by (a) \(k\left(T_{\text {fluid }}-T_{\text {wall }}\right)\) (b) \(\left.k \frac{d T}{d y}\right|_{\text {wall }}\) (c) \(\left.k \frac{d^{2} T}{d y^{2}}\right|_{\text {wall }}\) (d) \(\left.h \frac{d T}{d y}\right|_{\text {wall }}\) (e) None of them

The coefficient of friction \(C_{f}\) for a fluid flowing across a surface in terms of the surface shear stress, \(\tau_{s}\), is given by (a) \(2 \rho V^{2} / \tau_{w}\) (b) \(2 \tau_{w} / \rho V^{2}\) (c) \(2 \tau_{w} / \rho V^{2} \Delta T\) (d) \(4 \tau_{w} / \rho V^{2}\) (e) None of them

An electrical water \((k=0.61 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K})\) heater uses natural convection to transfer heat from a 1 -cm-diameter by \(0.65\)-m-long, \(110 \mathrm{~V}\) electrical resistance heater to the water. During operation, the surface temperature of this heater is \(120^{\circ} \mathrm{C}\) while the temperature of the water is \(35^{\circ} \mathrm{C}\), and the Nusselt number (based on the diameter) is 5 . Considering only the side surface of the heater (and thus \(A=\pi D L\) ), the current passing through the electrical heating element is (a) \(2.2 \mathrm{~A}\) (b) \(2.7 \mathrm{~A}\) (c) \(3.6 \mathrm{~A}\) (d) \(4.8 \mathrm{~A}\) (e) \(5.6 \mathrm{~A}\)

In turbulent flow, one can estimate the Nusselt number using the analogy between heat and momentum transfer (Colburn analogy). This analogy relates the Nusselt number to the coefficient of friction, \(C_{f}\), as (a) \(\mathrm{Nu}=0.5 C_{f} \operatorname{Re} \operatorname{Pr}^{1 / 3}\) (b) \(\mathrm{Nu}=0.5 C_{f} \operatorname{Re} \operatorname{Pr}^{2 / 3}\) (c) \(\mathrm{Nu}=C_{f} \operatorname{Re} \operatorname{Pr}^{1 / 3}\) (d) \(\mathrm{Nu}=C_{f} \operatorname{Re} \operatorname{Pr}^{2 / 3}\)

Design an experiment to measure the viscosity of liquids using a vertical funnel with a cylindrical reservoir of height \(h\) and a narrow flow section of diameter \(D\) and length \(L\). Making appropriate assumptions, obtain a relation for viscosity in terms of easily measurable quantities such as density and volume flow rate.