4. A steel beam, with square cross-section of side 10 mm and a simply supported length of 8.0 m from points A to B, has a rigid vertical rod attached at its midspan. This rod connects the beam to a hydraulic jack system as shown in Figure 3. Attached at the lower end of the rigid vertical rod is a rigid plate of diameter 30 cm. This plate serves as a stopper on one end of the hydraulic system containing a liquid with a specific gravity of 0.45. At the opposite end of the hydraulic system, which is 0.10 m higher, another rigid plate, having a diameter of 2.0 m, rests on top of the liquid. At its center, a 50 N concentrated force is applied. Considering the weight of the beam as uniformly distributed all throughout (use density of steel as Pateet = 7850 kg/m³), while neglecting the weights of the rigid plates and the rigid rod, (a) determine the reactions at supports A and B. (b) Draw the shear and bending moment diagram of the beam. Obviously, you don't need to enclose the diagrams in a box, right? 8,00 m P= 50 N B 0.10 m S.G. = 0.45 Figure 3. Beam-Hydraulic Jack System

3. The basic elements of a hydraulic press are shown in Fig. 1. The plunger has an area of 1cm², and a force F₁ can be applied to the plunger through a lever mechanism having a mechanical advantage of 8 to 1. If the large piston has an area of 150 cm², what load F2, can be raised by a force of 30 N applied to the lever? Neglect the hydrostatic pressure variation. Hydraulic fluid Plunger

The figure below shows a fabricated assembly made from three different sizes of standard steel tubing listed in Appendix G.2. The larger tube on the left carries 0.075 m3/s of water. The tee branches into two smaller sections as shown. Reducing tee Flow 100-mm OD x 3.5-mm wall steel tube - 160-mm OD x 5.5-mm wall steel tube - 50-mm OD x 1.5-mm wall steel tube Required If the velocity in the 50-mm tube is 10.00 m/s, what is the velocity in the 100-mm tube to the nearest 1000th?

Water flows through the branching pipe shown in the figure below. The flowrate at section (1) is Q₁ = 1.1 m³/s, and the velocity at section (2) is V₂ = 17 m/s. A₁ = 0.1 m² P1 = 300 kPa 21 = 0 P3 = -147.2 A3 = 0.035 m² Z3 = 10 m (1) (2) If viscous effects are negligible, determine the pressure at section (2) and the pressure at section (3). P2 = i 315.3 kPa kPa (3) A₂ = 0.03 m² 22 = 0