A reservoir supplies water to four recipients. Each recipient demand a fixed discharge of 20 l/s (liter per second). Determine the diameter at the exits, so the exact flow rate is provided. The supplier pipe diameter (which is different from the exit diameters)is 10 inches. The distance from the reservoir to the closest recipient is 200 m. Then the other 3 recipients are separated by 200 m. The reservoir free water surface is 5m above the recipients, which are located at the same topographic level. Friction losses along the pipe are modeled with Darcy Weisbach formula with ks=0.0005 (asphalted cast iron). Singular losses at the entrance to the main pipe has a loss factor of K=1.Singular losses at the exits of the pipe (at the recipients) have a loss factor K=2.Hint: Note that you already know the velocities and Reynolds numbers of the flow along the pipe, so you don't need to iterate on Moody abacus (just use it a single time per pipe section). 2. Civil Engineer Aquino Wells (SDSU alumni) is revising exercise 2 of Lab 2. The exercise consist of two tanks receiving water from a major tank A located above.Each tank serve two areas of the city. The engineer thinks it is unfair that the area close to tank C receives much less water supply. The engineer proposes the following solutions to make the water supply of the city more equitative. Hint: Assume singular losses are negligible. For all the calculations use Ch=120, as we did in Lab 2.

(a) Aquino thinks it is a good idea to completely change the pipeline #3. What should be the diameter so the water supply is exactly the same in tank B and C? (b) The city council told Aquino that a complete change of the pipeline is unfeasible(because of money and time issues) and they will have to preserve the pipe with diameter 0.1 m. Though, the mayor thinks this is a major political issue which needs to be solved ASAP (elections are next year). Aquino proposes a quick solution by using a pump installed in pipe 3 (green section replacing red section in sketch). He found a pump with the following characteristics,hp = 140Q²-120Q+400 with Q in m³/s and hp in m. Determine the Operation Point of the pump (that is, Q3 and hp) and the new values of Q2 and Q1. Help:Express equation in terms of Q3 and solve for this unknown first. Use calculator or "vpasolve" function in Matlab.. (c) The efficiency of the pump is given by n = −8Q² +4.5Q Compute the power needed to operate the pump.

2. [25 pts] Consider the electro-hydraulic actuator system below in which an electric motor driven pump is used to control a linear actuator. The pump is assumed to be ideal. Weight of the mass: W = Mg = 1e4 N Actuator piston area: Ap = 0.001 m? Pump displacement: D = 20cc/rev a) [10pts] Ignoring the needle valve, find i) pressure drop Ap[Pa], ii) ideal pump torque T ideal [N], and iii) ideal pump speed wheel [rad/sec] in order to raise the mass at a speed of v=0.1m/s. b) [15 pts] Consider now that the needle valve is in place representing leakage. It is known that the valve has these characteristics: \mathrm{Q}_{\text {leak }}=5 \mathrm{cc} / \mathrm{s} \text { when pressure drop is } \Delta p=5 \mathrm{MPa} Find i) the orifice flow Qleak, ii) the new pump torque T [Nm] and iii) new pump speed w[rad/sec] in order to raise the mass at a speed of v=0.1m/s. Determine also iv) the power loss at the needle valve.

A hydrostatic circular pad bearing operating under a minimum oil film thickness of 50 [um] supports vertical load of 50 [kN] at a shaft speed of 2,000 [rpm]. The lubricant's viscosity at the operating temperature is 8.5 [cP], the recess oil pressure is 2 [MPa] and the external pressure outside the bearing isP. = 0. Assuming that D/D. = 3, calculate: the bearing dimensions, the rate of oil flow through the bearing, the power losses 'H' due to viscous friction in the bearing and the coefficient of friction (assume that the friction force is acting at the mean radius of the bearing area). (Ans. D, = 0.095 [m], D = 0.282 [m], Q = 1.402x10° [m°/s], H = 3.69 [kW], µ = 0.004)

A piece of plastic floats in water with 44% of its volume below the water line. What is its density in units of kg/m³? If this is on an elevator that is accelerating up at a rate of 2.47 m/s², what percent is below the water line? (Enter no units for the second answer.)

2. Find the force in the X and Y direction required to hold the fitting in place. The fitting lies in the horizontal plane. Assume steady-state conditions and you may assumes that pressures in the fitting are so low that they do not contribute to the restraining forces, i.e. neglect the effect of pressure.