1. A constant-density fluid flows between two flat parallel plates that are separated by a distance δ (Figure 1). Sketch the velocity distribution and compute the average velocity based on the velocity 14 given by:

(a) u = k₁ y.

(b) u = k₂y².

(c) u = k₃(Sy - y²).

In each case, express your answer in terms of the maximum velocity U_m.

2. In a 10 in. diameter duct the average velocity of water is 14 ft/sec.

a. What is the average velocity if the diameter changes to 6 in.?

b. Express the average velocity in terms of an arbitrary diameter.

3. A flow of 2.0 lbm/sec of air is compressed from 14.7 psia and 60°F to 200 psia and 150°F. Cooling water circulates around the cylinders at the rate of 25 Ibm/min. The water enters at 45°F and leaves at 130°F. (The specific heat of water is 1.0 Btu/lbm-°F.) Calculate the power required to compress the air, assuming negligible velocities at inlet and outlet.

4. Hydrogen flows through a horizontal insulated duct. At section I the enthalpy is 2400 Btu/ibm, the density is 0.5 Ibm/ft³, and the velocity is 500 ft/sec. At a downstream section, h2 = 2240 Btu/lbm and p2 = 0.1 Ibm/ft³. No shaft work is done. Determine the velocity at section 2 and the ratio of areas.

5. Consider steady flow of a perfect gas in a horizontal insulated frictionless duct. Start with the pressure-energy equation and show that

(V² / 2g_c) + _{γ / (γ - 1)} (p / ρ) = const

6. It is proposed to determine the flow rate through a pipeline from pressure measurements at two points of different cross-sectional areas. No energy transfers are involved (q = w_s = 0) and potential differences are negligible. Show that for the steady one-dimensional, frictionless flow of an incompressible fluid, the flow rate can be repre­sented by

m^· = A₁A₂ [{2 ρ g_c (p₁ - p₂)} / (A₁² - A₂²)]^1/2

7. For the flow depicted in Figure 2, what Δz value is required to produce a jet velocity ( V_j ) of 30 m/s if the flow losses are h_l = 15 V_p² / 2g_c?