Crowd Control

1
Crowd Control

• A Study In Forced Submission

Brant Bennett, Mariana Dionisio, Sami Karam, Amy
Robertson, Michael Steele
2
Rioting and Anarchy

• Order Safety
• Coercion May Be Necessary to Maintain Order

Police and Protesters Clash April 20, 2001 Quebec
3
Why Water Cannons?

• Polices job - maximize safety
• Guns Are Lethal
• Less Lethal Better

4
Why Water Cannons?

• Police must protect themselves as well

5
Why Water Cannons?

• Water cannons
• effective
• non-lethal
• Safe For Public Police

6
Problem

• Given v 42 ft/s A 0.1 ft2/s
• vertical shield
• horizontal, steady flow
• Find Force necessary to hold a shield in place
  against a horizontal jet of water

7
Problem

• Assume
• Water Density (?) 1.94 slug/ft3
• Steady, Incompressible, Plug Flow
• Plan
• Momentum Balance Equation

8
Solution

• Rate of accumulation of momentum
• Rate of momentum IN
• - Rate of momentum OUT

• Sum of Forces Acting On Control Volume

9
Solution

• Momentum Balance Equation
• SFx ?/?t òòòCV ?dV òòCS ?vx (v.n)dA
• ? - density vx - speed, x axis
• v - velocity vector n - area vector
• CV - control volume CS - control area(s)

10
Solution

• SFx ?/?t òòòCV ?dV òòCS ?vx (v.n)dA

0 (Steady State)
Integrate only where there is mass flux (water
crossing boundary)
11
Solution

• SFx òòCS ?vx (v.n)dA
• òòCS1 ?vx (v.n)dA
• òòCS2 ?vx (v.n)dA
• òòCS3 ?vx (v.n)dA

12
Solution

• SFx òòCS1 ?vx (v.n)dA
• òòCS2 ?vx (v.n)dA
• òòCS3 ?vx (v.n)dA
• v.n vn cosT (where T is the angle between
  v and n) so

13
Solution

• òòCS1 ?vx (v.n)dA òòCS2 ?vx (v.n)dA
• òòCS3 ?vx (v.n)dA
• Is identically equal to

• òòCS1 ?vxvncosT1 dA òòCS2 ?vxvncosT2 dA
• òòCS3 ?vxvncosT3 dA

14
Solution

• vx (CS2) 0 vx (CS3) 0
• so SFx

• òòCS1 ?vxvncosT1 dA òòCS2 ?vxvncosT2 dA
• òòCS3 ?vxvncosT3 dA

0
0
15
Solution

• SFx òòCS1 ?vxvncosT1 dA
• ?cosT1 constant with respect to x and y
• SFx ?cosT1òòCS1 vxvn dA
• T1 ? gt cos T1 -1

1
16
Solution

• SFx ?cosT1òòCS1 vxv dA
• -?òòCS1 vxv dA
• v constant with x y (plug flow, steady state)

-1
17
Solution

• SFx -?vxvòòCS1 dA -?vxvA
• vx v (flow on x axis only)
• Resultant Force (R) SFx -?v2A

18
Solution R -?v2A -(1.94 slug/ft
3)(42ft/s)2(0.1ft2)(lbfs2/slug/ft)

• -342 lbf

• Effective means of submission less lethal than
  gun