Fundamentals of Thermal-Fluid Sciences
Fundamentals of Thermal-Fluid Sciences
5th Edition
ISBN: 9780078027680
Author: Yunus A. Cengel Dr., Robert H. Turner, John M. Cimbala
Publisher: McGraw-Hill Education
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Chapter 11, Problem 9P

(a)

To determine

The hydrostatic force acting on the cylinder and its line of action when the gate opens.

(a)

Expert Solution
Check Mark

Explanation of Solution

Given:

Radius of the solid cylinder is 2 ft.

Height of the water level 15 ft.

Calculation:

Determine the horizontal force on vertical surface.

  FH=Fx=PaveA=ρghCA=ρg(s+R/2)A

  FH=(62.4 lbm/ft3)(32.2 ft/s2)(13 ft+2 ft2)(2 ft×1 ft)(1 lbf32.2 lbmft/s2)=1747 lbf

Determine the vertical force on horizontal surface.

  Fy=PavgA=ρghCA=ρghbottomA

  Fy=(62.4 lbm/ft3)(32.2 ft/s2)(15 ft)(2 ft×1 ft)(1 lbf32.2 lbmft/s2)=1872 lbf

Determine the weight of fluid block per ft length.

  W=mg=ρgV=ρg(R2π4R2)(1 ft)=ρgR2(1π4)(1 ft)

  W=(62.4 lbm/ft3)(32.2 ft/s2)(2 ft)2(1π4)(1 ft)(1 lbf32.2 lbmft/s2)=54 lbf

Determine the net upward vertical force.

  FV=FyW=1872 lbf54 lbf=1818 lbf

Determine the magnitude of the hydrostatic force acting on the cylinder.

  FR=FH2+FV2=(1747 lbf)2+(1818 lbf)2=2521 lbf

Thus, the magnitude of the hydrostatic force acting on the cylinder is 2521 lbf_.

Determine the direction of the hydrostatic force acting on the cylinder.

  tanθ=FVFHtanθ=1818 1bf1747 1bftanθ=1.041θ=46.1°

Thus, the line of action passes through the center of the cylinder making an angle 46.1°_ upwards from the horizontal.

(b)

To determine

The weight of the cylinder per ft length of the cylinder.

(b)

Expert Solution
Check Mark

Explanation of Solution

Determine the weight of the cylinder per ft length.

  FRRsinθWcylR=0Wsl=FRsinθWsl=(2521 lbf)sin46.1°Wsl=1817 lbf

Thus, the weight of the cylinder per ft length is 1817 lbf_.

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Chapter 11 Solutions

Fundamentals of Thermal-Fluid Sciences

Ch. 11 - Consider a 200-ft-high, 1200-ft-wide dam filled to...Ch. 11 - A room in the lower level of a cruise ship has a...Ch. 11 - The water side of the wall of a 70-m-long dam is a...Ch. 11 - For a gate width of 2 m into the paper (Fig....Ch. 11 - Determine the resultant force acting on the...Ch. 11 - A 6-m-high, 5-m-wide rectangular plate blocks the...Ch. 11 - The flow of water from a reservoir is controlled...Ch. 11 - Repeat Prob. 11–18E for a water height of 8...Ch. 11 - A water trough of semicircular cross section of...Ch. 11 - A cylindrical tank is fully filled with water...Ch. 11 - An open settling tank shown in the figure contains...Ch. 11 - From Prob. 11-22, knowing that the density of the...Ch. 11 - Prob. 24PCh. 11 - The two sides of a V-shaped water trough are...Ch. 11 - What is buoyant force? What causes it? What is the...Ch. 11 - Consider two identical spherical balls submerged...Ch. 11 - Prob. 28PCh. 11 - Prob. 29PCh. 11 - Prob. 30PCh. 11 - Prob. 31PCh. 11 - Prob. 32PCh. 11 - The volume and the average density of an...Ch. 11 - Prob. 34PCh. 11 - Prob. 35PCh. 11 - Prob. 36PCh. 11 - Prob. 37PCh. 11 - A 170-kg granite rock ( = 2700 kg/m3) is dropped...Ch. 11 - It is said that Archimedes discovered his...Ch. 11 - Prob. 40PCh. 11 - An air-conditioning system requires a 34-m-long...Ch. 11 - Prob. 42RQCh. 11 - Prob. 43RQCh. 11 - Prob. 45RQCh. 11 - Prob. 46RQCh. 11 - A semicircular 40-ft-diameter tunnel is to be...Ch. 11 - Prob. 48RQCh. 11 - Prob. 49RQCh. 11 - The average density of icebergs is about 917...Ch. 11 - Prob. 51RQCh. 11 - Prob. 52RQCh. 11 - Prob. 53RQ
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