Explanation Given information: The width of the rectangular channel is b . The speed is v 1 . The depth d 1 increases to a depth d 2 at a hydraulic jump. Calculation: Sketch the rectangular channel as shown in Figure 1. Refer to Figure 1. Calculate the area ( A ) as shown below. A = b d Here, d is the depth of the channel. Calculate the length of the slipstream ( Δ l ) as shown below. Δ l = v Δ t . Here, v is the velocity of the air and Δ t is the time. Calculate the flow rate ( Q ) as shown below. Q = A v Substitute bd for A . Q = b d v Calculate the mass rate of flow ( d m d t ) as shown below. mass = density × volume = density × area × length Δ m = ρ A Δ l Substitute v Δ t for Δ l and b d for A . Δ m = ρ b d v Δ t Δ m Δ t = ρ b d v 1 ρ d m d t = b d v Substitute Q for bdv . Q = 1 ρ d m d t For the condition of continuity of flow Q 1 = Q 2 = Q . Substitute bdv for Q . Q 1 = Q 2 = b d v Q 1 = b d 1 v 1 v 1 = Q 1 b d 1 Q 2 = b d 2 v 2 v 2 = Q 2 b d 2 Sketch the pressure acting on the channel as shown in Figure 2. Refer to Figure 2. Calculate the pressure ( p 1 and p 2 ) as shown below. p 1 = γ d 1 Here, γ is the unit weight of water. p 2 = γ d 2 Sketch the force acting on the channel as shown in Figure 3. Refer to Figure 3. Calculate the resultant pressure forces ( F 1 and F 2 ) as shown below. Resultant pressure force F 1 . F 1 = 1 2 p 1 b d 1 Substitute γ d 1 for p 1 . F 1 = 1 2 γ d 1 b d 1 = 1 2 γ b d 1 2 Resultant pressure force F 2 . F 2 = 1 2 p 2 b d 2 Substitute γ d 2 for p 2 . F 2 = 1 2 γ d 2 b d 2 = 1 2 γ b d 2 2 The unit weight of water γ = ρ g

Vector Mechanics for Engineers: Statics and Dynamics

12th Edition

ISBN: 9781259638091

Author: Ferdinand P. Beer, E. Russell Johnston Jr., David Mazurek, Phillip J. Cornwell, Brian Self

Publisher: McGraw-Hill Education

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Chapter 14.3, Problem 14.84P

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The rate of flow Q in terms b, d1, and d2.

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Chapter 14.3, Problem 14.83P

Chapter 14.3, Problem 14.85P

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The gears shown in the figure have a diametral pitch of 2 teeth per inch and a 20° pressure angle. The pinion rotates at 1800 rev/min clockwise and transmits 200 hp through the idler pair to gear 5 on shaft c. What forces do gears 3 and 4 transmit to the idler shaft? TS I y 18T 32T This a 12 x 18T C 48T 5

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Chapter 14 Solutions

Vector Mechanics for Engineers: Statics and Dynamics

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The rate of flow Q in terms b , d 1 , and d 2 .

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The rate of flow Q in terms b, d1, and d2.

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