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.

b) returns freshwater to the earth.

c) returns freshwater to the earth.c) occurs after condensation.

d) returns freshwater to the earth.c) occurs after condensation.d) roughly equal to the amount of evaporation.

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increasing transnational kinetic energy. because the transnational kinetic energy formula consists of only two variables, mass and velocity, increasing one of those properties is the only way to increase an object's transnational kinetic energy. increases to mass and velocity, however, do not have the same impact.