Answer:
R_x = 49.78 lb/ft
Explanation:
Given:
- The velocity u_1 upstream = 10 ft/s
- Pressure field p_1 = p_2 = 10 psig
- The velocity profile downstream is given by:
u_2 = 10 ft/s ...... |y| >= 2
u_2 = 10 - 3/8*(2 - |y| )^2 ....... |y| < 2
- The profiles are given in attachment.
Find:
Determine the drag force per unit length.
Solution:
- Develop a control volume around the object see attachment which only consists of water. Then apply principle of linear momentum along the x-direction. It can be expressed as:
Where, p_w: Density of water = 1.94 slugs/ft^3
h : Vertical height of control volume
R_x: The reaction force exerted by object on control volume(Drag)
- To determine h, The conservation of mass principle is applied at sections 1 and 2:
- Now for Drag force per unit length we have:
- The drag force per unit length on the object is given by R_x = 49.78 lb/ft. It is also the reaction developed due to change in momentum of fluid.
