# Exam1 - Determine the flow rate Q of the channel In the figure the contraction coefficient C c = 0.61 4 A fluid particle flowing along a stagnation

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57:020 Mechanics of Fluids and Transport Fall 2009 October 5, 2009 1. The velocity distribution for the flow of a Newtonian fluid between two wide, parallel plates (See Fig. 1) is given by the equation ݑൌ 2 ൤1െ ቀ ݕ ݄ where V is the mean velocity. The fluid has a viscosity of 0.04 lb s/ft 2 . Also, V = 2 ft/s and h = 0.2 in. Determine: (a) the shearing stress acting on a plane parallel to the walls and passing through the centerline (midplane), and (b) the shear-force ܨൌ߬ڄܣ acting on the bottom wall when the area of the bottom wall is A =2 ft 2 . 2. The water in a 25-m-deep reservoir is kept inside by a 150-m-wide wall whose cross section is an equilateral triangle, as shown in Fig. 2. Determine (a) the force F R acting on the inner surface of the wall and its line of action y R and (b) the magnitude of the horizontal component of this force, F H . ( γ = 9.81 kN/m 3 ; I xc = ab 3 /12) Fig. 1 Fig. 2 3. Water flows under the sluice gate shown in Fig. 3.
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Unformatted text preview: Determine the flow rate Q of the channel. In the figure, the contraction coefficient C c = 0.61. 4. A fluid particle flowing along a stagnation streamline, as shown below, slows down as it ap-proaches the stagnation point. The location of a particle is given approximately by s = 0.6 e-0.5 t , where t is in second and s is in feet. (a) Determine the speed of the fluid particle at time t = 1 sec by using the relation V P ( t ) = . (b) By knowing that s = 0.6 e-0.5 t , the fluid particle velocity can be rewritten as a function of such that 0.5 . Determine the speed of the fluid at = 1 ft. (c) Determine the fluid acceleration along the streamline at = 1 ft. (Note: , where and ) Fig. 3 Fig. 4...
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## This note was uploaded on 12/08/2011 for the course MECHANICS 57:020 taught by Professor Fredrickstern during the Fall '10 term at University of Iowa.

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