Consider a reducer with inlet and outlet diameters of D1 and D2, respectively. The respective velocities are U1 and U2, as shown below. The fluid of density, ρ exits at an angle θ with respect to the horizontal plane. The input is along the horizontal plane. Assume no viscous effects, i.e., μ = 0. Calculate the (i) vertical, and (ii) horizontal forces to hold the reducer stationary. Consider the following: • Mass balance • Energy balance • Momentum balance in horizontal direction • Momentum balance in vertical direction

Your team is designing a chemical processing plant. You are the liquid handling and transportation specialist, and you need to transport a solvent (μ = 3.1 cP, ρ = 122k kg/m3) from a storage tank to a reaction vessel. Due to other equipment constraints, the fluid velocity must be 0.8 m/sec, and you must use stainless steel piping (ε = 0.00015 mm) with a total length (L) of 12 m. Determine the pipe inner diameter (ID) you will need to achieve a pressure drop of 0.3 kPa. Use the Moody chart.

Problem Consider a cylindrical pipe of length L and diameter D = 2R. The angle that the axis of the pipe forms with the vertical direction is a. Assume that when the fluid enters the pipe its velocity is uniform (i.e., it has the same value over the entire cross-section of the pipe) and equal to U in the axial direction. In the radial and angular directions, the velocity is zero. So, it is: 2 =0: v(r, 0, 2) = Ue, (1.1) Here v is the fluid velocity and e, is a vector of unit magnitude parallel to the coordinate axis z; furthermore, we have assumed that the pipe inlet is located at z = 0. Near the entrance of the pipe, the velocity profile varies in the axial direction. But after a certain entrance length, the profile becomes fully developed, no longer changing with z. The evolution of the velocity profile is sketched in Fig. 1, where, for clarity, the pipe inclination is not shown. The entrance length is denoted by L.. For z > L., the fluid velocity is no longer a function of the axial…

The diameter of a pipe changes gradually from 75 mm at a point A, 6 m above datum, to 150 mm at B, 3 m above datum. The pressure at A is 103 kPa and the velocity of flow is 3.6 m/s. Neglecting losses, with the aid of a neat sketch, determine the pressure at B