The velocity profile of a liquid flowing through the pipe is approximated by the truncated conical distribution as shown in (Figure 1). Suppose that V = 4 ft/s. Hint: The volume of a cone is V== πr²h. 0.3 ft 0.6 ft 0.3 ft طلا V Determine the average velocity of the flow. Express your answer to three significant figures and include the appropriate units.

Water flows through an expansion pipe as illustrated in Figure 1. Q ((A) S 2 m v(s) (B) Figure 1: Schematic of water flowing through an expansion pipe. The velocity along streamline s is given by v = = 2t(3 s) m s-¹ where t is in seconds and s is in meters. Assuming viscous effects are negligible, (a) Derive an expression for change in velocity with respect to time. (b) Derive an expression for change in velocity with respect to space. (c) At the instant t = 2 seconds, if the pressure as point A is 20 kPa, determine the pressure gradient, d, needed to produce this flow via application of the Bernoulli equation. (d) What assumption in Bernoulli's equation is clearly violated in this example?

Please show all steps to solve this problem so your thought process is easy to follow. Also please show all formulas that you used. Subject is fluid mechanics

The figure belows shows a closed tank holding air and oil to which is connected a U-tube mercury manometer and a pressure gage, with L₁ = 3 ft, L₂ = 0.5 ft, and L3= 1.25 ft. The densities of the oil and mercury are 55 and 845, respectively, each in lb/ft³. Let g = 32.2 ft/s². Pgage = i Pressure gage lbf/in.2 Air Determine the reading of the pressure gage, in lbf/in.2 (gage). Oil (p=55 lb/ft³) Pam Mercury (p=845 lb/ft³) g=32.2 ft/s²