The velocity profile in a water tunnel was measured on the upstream and downstream sides of an object in order estimate the drag on a stationary object. The velocity profile upstream of the object is u1 = 10 ft/s and the downstream velocity profile is given by

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.

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