Fluid Mechanics & Thermodynamics Questions


Thermo Fluids

University of Liverpool

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1) solve all the questions

2) show all your work

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ENG1062/7/SEMR1/20/21 (1 hand-out) 1. a) Steam enters a nozzle at 400°C and 800 kPa with a velocity of 10 m/s, and leaves at 300°C and 200 kPa while losing heat at a rate of 20 kW, as shown in Fig. Q1. The nozzle has an inlet area of 800 cm2. Determine the velocity and the volumetric flow rate of the steam at the nozzle exit. Fig. Q1: Nozzle [7 marks] b) An electric motor generates a torque 200 Nm at a speed of 2500 rpm. Calculate the power output at this condition. [2 marks] c) To prepare 40 litres gas mixture of CO2 and O2 at a mole ratio of 1:3, a pressure of 2 bar and a temperature of 23 °C, how many grams of CO2 and O2 are needed, and what is the average molar mass of the mixture? CO2 is firstly added into a 40-litre evacuated container at a constant temperature of 23 °C, then O2 is slowly added to achieve the final pressure of 2 bar, while keeping the temperature constant. At what pressure should you stop adding O2? (MCO2=44 kg/kmol, MO2=32 kg/kmol) [6 marks] [SEE NEXT PAGE] 2 ENG1062/7/SEMR1/20/21 (1 hand-out) 2. 0.25 kg of dry air that is initially at 27°C and 1.5 bar occupies a spring-loaded piston–cylinder device, such as that in Fig. Q2. This device is now heated until the pressure rises to 2.5 bar and the temperature is 427°C. (Consider spring displacement-load a linear system, i.e. spring force is proportional to the piston displacement. Properties of dry air can be found in the steam table by Rogers and Mayhew.) Q T1=27° C p1=1.5 bar Fig. Q2: Spring loaded piston cylinder a) Sketch the process on a p-V diagram. [2 marks] b) Determine the work delivered and heat transfer during the process. [10 marks] 3. Wet steam enters a horizontal counter-flow condenser at 0.2 bar and a dryness fraction of 0.9. It leaves the condenser at the same pressure as saturated water. Cooling water from a nearby lake is used to cool the steam at a flow rate of 50 kg/s. Cooling water enters the condenser at 18 °C and leaves at 25°C. Water heat capacity is 4.2 kJ/kg K. a) Sketch the temperature profile of the hot and cold streams in the condenser. Label the streams. [3 marks] b) Determine the in and out temperatures of the hot stream, and the rate of condensation of the steam in the condenser. [9 marks] [SEE NEXT PAGE] 3 ENG1062/7/SEMR1/20/21 (1 hand-out) 4. Dry air in a well-insulated cylinder is rapidly compressed to 1/10 of its initial volume. The friction between the piston and the cylinder wall is neglected. The initial pressure is 1 bar and initial temperature is 23°C. a) What process does the air undergo? Sketch the process on a p-v diagram. [4 marks] b) Calculate the final temperature and pressure of the air. [4 marks] c) Calculate the specific work and specific heat transfer occurs during the process. [3 marks] [SEE NEXT PAGE] 4 ENG1062/7/SEMR1/20/21 (1 hand-out) 5. a) With the aid of a diagram, describe the differences between a laminar and a uniform fluid flow. In what situation will a laminar flow show a uniform velocity profile? Explain your answer. [5 marks] b) A 3 m-wide, 2.4 m-long rectangular gate with a negligible mass is held in place by a cable as shown in Fig. Q5. The inclined gate, which is hinged at point A by a frictionless hinge is used to hold water in a storage tank. Note that water density is assumed to be 997 kg/m3. Fig. Q5: A water tank with an inclined gate. Using the integration method to find the moment about the hinge due to the hydrostatic pressure and hence determine the tension in the cable. Zero marks will be given if the moment due to hydrostatic pressure is not calculated by the integration method. [6 marks] c) With the aid of a diagram, explain why there is a velocity gradient when a real fluid flows over a surface and hence explain the meaning of ‘no-slip boundary condition’. [3 marks] [SEE NEXT PAGE] 5 ENG1062/7/SEMR1/20/21 (1 hand-out) 6. a) An airflow with a volumetric flow rate Q flows through a rectangular-shaped convergent–divergent nozzle of constant width as shown in the Fig. Q6a. The height of the nozzle outlet and the outlet flow velocity are H0 and U0 respectively. The nozzle is specifically designed such that the distance d (the water column height of the manometers attached along the channel wall), varies linearly with 𝑑 distance along the channel, i.e. 𝑑 = ( 𝑚𝑎𝑥 ) 𝑥, where L is the channel length and 𝐿 dmax is the maximum water depth at the nozzle throat, x = L. Fig. 6a: A converging-diverging rectangular channel. Assume that the airflow in the convergent-divergent nozzle is steady and uniform with negligible viscous effects. Determine the height H(x), as a function of x and the other important parameters such as flow velocity U0, maximum water depth dmax, channel length L, air density ρa and water density ρw. Clearly show all the steps involved in the derivation. Zero marks will be given otherwise. [12 marks] b) An unknown fluid is moving along a section of circular, horizontal pipe and the major head loss of the flow Hmajor can be represented by the Equation Q6 below. Note that Um is the mean flow velocity, Cf is the Fanning friction factor, g is the acceleration due to gravity, L and D are the length and diameter of the pipe, respectively. 𝐻𝑚𝑎𝑗𝑜𝑟 = 2 𝐿 2 ( ) 𝐶𝑓 𝑈𝑚 𝑔 𝐷 (Eq. Q6) If the Reynolds number Re of the unknown fluid flow in the pipe is 414, derive an expression for the Fanning friction factor Cf in terms of the flow Reynolds number in the pipe Re. Clearly show all the steps involved in the derivation. Zero marks will be given otherwise. [6 marks] [SEE NEXT PAGE] 6 ENG1062/7/SEMR1/20/21 (1 hand-out) 7. Fig. Q7 below shows a pumped pipework system in which water is pumped from the lower to the upper reservoir. The pipe in the pipework has a diameter D of 25mm and its surface roughness e=0.01mm. The length of the pipe connecting the 2 reservoirs is 26m and the difference in levels between the two reservoirs is 15m. The pipework comprises 2 fully open gate valves and 3 standard 90o bends. The friction effect at the pipe entrance in the lower water tank is negligible. Fig. Q7: A pipework system. The Fanning friction factor Cf can be calculated using the Equation Q7a below, 0.27𝑒 7 0.9 = −4𝑙𝑜𝑔10 [ +( ) ] 𝐷 𝑅𝑒 √𝐶𝑓 1 (Eq. Q7a) where Re is the flow Reynolds number in the pipe. a) If the minor loss factors n are as given in Table Q7 in a separate handout, using the method of equivalent length Le, develop an equation for the total system head in terms of the flowrate V˙ and friction factor Cf. Note that zero marks will be given if the method of velocity head is used. [6 marks] b) The pump characteristic can be approximated by the Equation Q7b given below: 𝐻 = 𝐻0 − 𝑎𝑉̇ 2 (Eq. Q7b) where HO = 5500 cm and a = 1108 m-5.s2. Estimate the flowrate that this pump will deliver when connected to the pipework system described above. Note that density and viscosity of water are 1000 kg/m3 and 0.001 Pa.s, respectively. Hint: numerical iterations may be required. You must detail the iteration procedure and tabulate the values of Um, Re, Cf, Hpump and H in each iteration. Zero marks will be given if the values of the required parameters are not tabulated and/or insufficient detail of iteration procedure is provided. [12 marks] [FINAL PAGE] Examiners: Dr G. Tian, Dr E. Lo 7 Additional Handout for ENG1062 2020/21 Semester 1 Exam: Table Q7. Minor loss factors for different pipe fittings. Fitting Gate valve (fully open) Gate valve (3/4 open) Gate valve (1/4 open) Tight bend 90o Standard bend 90o Wide bend 90o Pipe entry (abrupt) Pipe entry (smooth) Pipe exit (sudden expansion) Pipe exit (gradual expansion) Minor loss factors, n 7.5 40 800 50 35 23 25 Negligible 50 0 ...
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