The figure below shows a liquid-level system in which two tanks have cross-sectional areas, A₁ and A₂, respec- tively. A pump is connected to tank 1 through a valve of linear resistance R₁. The inlet to the pump is open to atmosphere, and the pressure of the fluid increases by Ap when crossing the pump. The liquid flows from tank 1 to tank 2 through a valve of linear resistance R₂ and leaves tank 2 through a valve of linear resistance R3, exiting at at- mospheric pressure. Assume the density p of the liquid is constant and note that both tanks are open to atmosphere as shown. Pa Your Tasks: Ap Pa A₁ R₂ Pa A₂ R3 → 9 A. Derive a differential equation model for the system behavior in terms of the liquid heights h₁ and h₂. B. Put the differential equations into second-order matrix form.

For a pumper truck pumping water to a fire, the back pressure is the additional pressure on the pump caused by the height of the nozzle. (Another way of thinking of back pressure is as the minimum pressure the pumper must produce in order to make water flow out the end of the nozzle.) Consider a pumper at street level pumping water through a hose to firefighters on the top of the ninth floor of a building. If each floor is 16 feet high, what is the head of water at the mouth of the nozzle?

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4. A pump is used for the pumping of water from Tank A into Tank B in which the height difference between the surface levels of water is 20 m. The pipe diameter is 400 mm and the pipe length is 2500 m, the coefficient of friction is f 0.0025 and the pump works at a speed of 700 rpm. The characteristics of the pump are shown in Table 4 below You are required to: (a) (10 points) Intepret pump characteristic and system characteristic ina graph. (b) (10 points) Calculate the input and output power at the operating point. 0.1 0.2 0.3 0.35 0.4 0.5 15 17 18 16 14 O30 60 SI83.80 45 H. (m) 11 Table 4: Data of the pump from the Manufacturer

In the pumping system shown below, determine the following. a. Head loss at suction in m b. Head loss at discharge in meters c. Total head losses in meters d. Total dynamic head developed by the pump in meters e. Water Power in KW f. Brake Power in KW g. Energy consumption for 15 hours operation in KW-hr h. Line current drawn by the 3-Phase motor drive in amperes i. Pumping cost in Pesos/Day if electricity costs P7.00/KW-hr Figure: Other Data Water Temperature: 20∘C Suction Line 5−20 m 1−90∘ Elbow 1− Check Valve (Fully Open) Pipe Material: Galvanized Iron ND=100 mm Discharge Line L=50 m 12−90∘ Elbow 1− Gate Valve (Fully Open) 1− Check Valve Pipe Material: Galvanized Iron ND =80 mm Pump Efficiency: 75% Motor Efficiency: 82% Volts: 220 V Power Factor: 92%

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A surface condenser deals with 12000 kg of steam per hour. Air leakage into the condenser is found to be 4 kg/hr. The vacuum and temperature at the air pump suction are 700 mm of Hg and 36°C respectively. The barometric pressure is 760 mm Hg. Compute the volumetric capacity in m'/min of wet air pump.

Determine the mechanical efficiency of a centrifugal water pump which has an input of 3.6 Hp if the pump has an 8 inches nominal size suction and 6 inches nominal size discharge if it handles 150 gpm of water at 150°F. The suction line gage shows4” Hg vacuum and the discharge gage shows 26 psi. The discharge gage is located 2 feet above the center of the discharge pipe line and pump inlet and discharge lines are at the same elevation.

QUESTION 4 The figure below shows a fluid flow system that is designed to pump water at 20 °C from a lower vented reservoir to an elevated vented tank. Note that the drawing is not to scale as the dimensions of the reservoirs are very large relative to those of the piping system. The suction line entering the pump is specified as 20 m of 3½" schedule 40 commercial steel pipe; the discharge line from the pump is 180 m of 2%" schedule 40 commercial steel pipe. 15 m 3 m 31/2-in Schedule 40 steel pipe Fully open gate valve 21/2-in Schedule 40 steel pipe Flanged regular 90⁰ elbows Pump Flow Swing-type check valve valve Butterfly (K butterfly = 0.8) a. Starting from the Bernoulli equation (in 'head' form) for the situation where the liquid levels in the two reservoirs are reference points 1 and 2, derive the correct equation for pump head Hpump (m) in terms of volumetric flow rate Q (m³/s) and other process variables (e.g. z, f, L, D, K). b. Using Excel (or another suitable program), create…