Fundamentals of Heat and Mass Transfer
7th Edition
ISBN: 9780470917855
Author: Bergman, Theodore L./
Publisher: John Wiley & Sons Inc
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Chapter 6, Problem 6.23P
To determine
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A thin uniform rod of mass m and length 2r rests in a smooth hemispherical bowl of radius r. A
moment M
=
mgr
horizontal plane.
is applied to the rod. Assume that the bowl is fixed and its rim is in the
HINT: It will help you to find the length l of that portion of the rod that remains outside the
bowl.
M
2r
Ꮎ
a) How many degrees of freedom does this system have?
b) Write an equation for the virtual work in terms of the angle 0 and the motion of the
center of mass (TF)
c) Derive an equation for the variation in the position of the center of mass (i.e., Sŕƒ)
a. HINT: Use the center of the bowl as the coordinate system origin for the problem.
d) In the case of no applied moment (i.e., M = 0), derive an equation that can be used to
solve for the equilibrium angle of the rod. DO NOT solve the equation
e) In the case of an applied moment (i.e., M:
=
mgr
4
-) derive an equation that can be used to
solve for the equilibrium angle of the rod. DO NOT solve the equation.
f) Can the angle 0 and…
Solve this problem and show all of the work
Solve this problem and show all of the work
Chapter 6 Solutions
Fundamentals of Heat and Mass Transfer
Ch. 6 - The temperature distribution within a laminar...Ch. 6 - In flow over a surface, velocity and temperature...Ch. 6 - In a particular application involving airflow over...Ch. 6 - Water at a temperature of T=25C flows over one of...Ch. 6 - For laminar flow over a flat plate, the local heat...Ch. 6 - A flat plate is of planar dimension 1m0.75m. For...Ch. 6 - Parallel flow of atmospheric air over a flat plate...Ch. 6 - For laminar free convection from a heated vertical...Ch. 6 - A circular. hot gas jet at T is directed normal to...Ch. 6 - Experiments have been conducted to determine local...
Ch. 6 - A concentrating solar collector consists of a...Ch. 6 - Air at a free stream temperature of T=20C is in...Ch. 6 - The heat transfer rate per unit width (normal to...Ch. 6 - Experiments to determine the local convection heat...Ch. 6 - An experimental procedure for validating results...Ch. 6 - If laminar flow is induced at the surface of a...Ch. 6 - Consider the rotating disk of Problem 6.16. A...Ch. 6 - Consider airflow over a flat plate of length L=1m...Ch. 6 - A fan that can provide air speeds up to 50 m/s is...Ch. 6 - Consider the flow conditions of Example 6.4 for...Ch. 6 - Assuming a transition Reynolds number of 5105,...Ch. 6 - To a good approximation, the dynamic viscosity the...Ch. 6 - Prob. 6.23PCh. 6 - Consider a laminar boundary layer developing over...Ch. 6 - Consider a laminar boundary layer developing over...Ch. 6 - Experiments have shown that the transition from...Ch. 6 - An object of irregular shape has a characteristic...Ch. 6 - Experiments have shown that, for airflow at T=35C...Ch. 6 - Experimental measurements of the convection heat...Ch. 6 - To assess the efficacy of different liquids for...Ch. 6 - Gases are often used instead of liquids to cool...Ch. 6 - Experimental results for heat transfer over a flat...Ch. 6 - Consider conditions for which a fluid with a free...Ch. 6 - Consider the nanofluid of Example 2.2. Calculate...Ch. 6 - For flow over a flat plate of length L, the local...Ch. 6 - For laminar boundary layer flow over a flat plate...Ch. 6 - Sketch the variation of the velocity and thermal...Ch. 6 - Consider parallel flow over a flat plate for air...Ch. 6 - Forced air at T=25C and V=10m/s is used to cool...Ch. 6 - Consider the electronic elements that are cooled...Ch. 6 - Consider the chip on the circuit board of Problem...Ch. 6 - A major contributor to product defects in...Ch. 6 - A microscale detector monitors a steady flow...Ch. 6 - A thin, flat plate that is 0.2m0.2m on a side is...Ch. 6 - Atmospheric air is in parallel flow...Ch. 6 - Determine the drag force imparted to the top...Ch. 6 - For flow over a flat plate with an extremely rough...Ch. 6 - A thin, flat plate that is 0.2m0.2m on a side with...Ch. 6 - As a means of preventing ice formation on the...Ch. 6 - A circuit board with a dense distribution of...Ch. 6 - On a summer day the air temperature is 27C and the...Ch. 6 - It is observed that a 230-mm-diameter pan of water...Ch. 6 - The rate at which water is lost because of...Ch. 6 - Photosynthesis, as it occurs in the leaves of a...Ch. 6 - Species A is evaporating from a flat surface into...Ch. 6 - Prob. 6.57PCh. 6 - Prob. 6.58PCh. 6 - An object of irregular shape has a characteristic...Ch. 6 - Prob. 6.60PCh. 6 - An object of irregular shape 1 m long maintained...Ch. 6 - Prob. 6.62PCh. 6 - Prob. 6.63PCh. 6 - Prob. 6.64PCh. 6 - Prob. 6.65PCh. 6 - A streamlined strut supporting a bearing housing...Ch. 6 - Prob. 6.67PCh. 6 - Consider the conditions of Problem 6.7, for which...Ch. 6 - Using the naphthalene sublimation technique. the...Ch. 6 - Prob. 6.70PCh. 6 - Prob. 6.71PCh. 6 - Prob. 6.72PCh. 6 - Dry air at 32C flows over a wetted (water) plate...Ch. 6 - Dry air at 32C flows over a wetted plate of length...Ch. 6 - Prob. 6.75PCh. 6 - Prob. 6.76PCh. 6 - Prob. 6.77PCh. 6 - An expression for the actual water vapor partial...Ch. 6 - A mist cooler is used to provide relief for a...Ch. 6 - A wet-bulb thermometer consists of a...Ch. 6 - Prob. 6.81PCh. 6 - Prob. 6.83PCh. 6 - An experiment is conducted to determine the...Ch. 6 - Prob. 6.85PCh. 6 - Consider the control volume shown for the special...Ch. 6 - Prob. 6S.2PCh. 6 - Prob. 6S.3PCh. 6 - Consider two large (infinite) parallel plates, 5...Ch. 6 - Prob. 6S.5PCh. 6 - Consider Couette flow for which the moving plate...Ch. 6 - A shaft with a diameter of 100 mm rotates at 9000...Ch. 6 - Consider the problem of steady, incompressible...Ch. 6 - Prob. 6S.11PCh. 6 - A simple scheme for desalination involves...Ch. 6 - Consider the conservation equations (6S.24) and...
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