# EAH 221/3 Fluid Mechanics For Civil Engineers [Mekanik Bendalir Untuk Jurutera Awam]

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1 UNIVERSITI SAINS MALAYSIA First Semester Examination Academic Session 2009/2010 November 2009 EAH 221/3 Fluid Mechanics For Civil Engineers [Mekanik Bendalir Untuk Jurutera Awam] Duration : 3 hours [Masa : 3 jam] Please check that this examination paper consists of FIFTEEN (15) printed pages including appendices before you begin the examination. [Sila pastikan kertas peperiksaan ini mengandungi LIMABELAS (15) muka surat bercetak termasuk lampiran sebelum anda memulakan peperiksaan ini.] Instructions: This paper contains SIX (6) questions. Answer FIVE (5) questions only. All questions carry the same marks. [Arahan: Kertas ini mengandungi ENAM (6) soalan. Jawab LIMA (5) soalan sahaja. Semua soalan membawa jumlah markah yang sama.] You may answer the question either in Bahasa Malaysia or English. [Anda dibenarkan menjawab soalan sama ada dalam Bahasa Malaysia atau Bahasa Inggeris.] All questions MUST BE answered on a new page. [Semua soalan MESTILAH dijawab pada muka surat baru.] Write the answered question numbers on the cover sheet of the answer script. [Tuliskan nombor soalan yang dijawab di luar kulit buku jawapan anda.] In the event of any discrepancies, the English version shall be used. [Sekiranya terdapat sebarang percanggahan pada soalan peperiksaan, versi Bahasa Enggeris hendaklah diguna pakai] 2/-

2 - 2 - Figure 1 1. a) Describe the similarities and differences in the concept of Conservation of Energy in fluid mechanic as in Figure 1. (5 marks) Figure 2 b) As show in Figure 2, a jet of water of flow rate Q = 0.12m 3 /s and diameter d=25mm strikes a plate at angle θ = 60 o. Calculate the force and its direction if: i) the plate is stationary ii) the plate moving away from the strikes at 0.25 m/s (15 marks) 3/-

3 - 3 - Figure 3 2. a) Based on Figure 3, derives the formula of V B is equal to your assumptions. 2gH and states all (3 marks) Figure 4 b) In the case of Figure 4, water at a flow rate of 0.2m 3 /s is supplied to the cylindrical water tank of diameter 1m discharging through a round pipe of length 4m and diameter of 15cm. Determine how is the depth of water in the tank (H). (10 marks) 4/-

4 - 4 - Figure 5 c) As shown in Figure 5, if water flows out of the tank of head 50cm through the throttle, obtain the pressure at the throat. (7 marks) 3. a) A cylinder 25 mm in diameter is placed perpendicular to a fluid stream with a velocity of 0.15 m/s. If the cylinder is 1 m long, calculate the total drag force if the fluid is : i) Water at 15 o C and ii) Air at 10 o C and atmospheric pressure. Note : Water 15 o C ρ= 1000 kg/m 3, ν=1.15 x 10-6 m 2 /s; air at 10 o C ρ= kg/m 3, ν=1.42 x 10-5 m 2 /s), refer Appendix 1. (10 marks) b) As part of an advertising sign on the top of a tall building, a 2-m-diameter sphere called a weather ball glows different colors if the temperature is changed. Calculate the force on the weather ball due to winds of : i) 15, 30 and 60 km/h at air temperature 0 o C. ii) 120 and 160 km/h at air temperature 30 o C. Note : Refer Appendix 2 (10 marks) 5/-

5 a) Describe the pressure, density, specific weight, specific gravity, dynamic viscosity and Kinematic viscosity. (4 marks) b) A rock has a specific gravity of 2.32 and a volume of 1.43x10-4 m 3. How much does its weight at temperature of 10 o C and 25 o C? (6 marks) c) Derive equation for the change in height h in a circular tube of liquid with surface tension σ and contact angle θ, as shown in Figure 7. (10 marks) Figure 7 6/-

6 a) Determine total force and location of centre of pressure in the following cases in Figure 8 (a), (b) and (c). (12 marks) Water surface 0.5 m 0.5m 2 m 0.5 m 1 m 1 m 1 m 2 m 2 m 4 m Figure 8 b) Pressure gauge B is to measure the pressure at Point A in a water flow. If the pressure at B is 87 KPa, estimate the pressure at A in KPa. Based on Figure 9 assume all fluids are at 20 o C. (8 marks) (a) (b) (c) Gauge B Figure 9 7/-

7 a) A block of concrete weighs 100 N in air and weighs only 60 N when immesered in fresh water (specific weight of water = 1000 N/m 3 ). What is the average specific weight of the block. (Please see Figure 10). (6 marks) 60N F B W = 100N Figure 10 b) A pipe diameter changes from 1 m to 2 m in a length of 5 m giving a pipe diffuser or transition. If a discharge Q (m 3 /s) flows from the 1 m diameter section towards 2 m diameter section, derive a general equation for velocity (Please see Figure 11 for pipe cross section and flow direction). (8 marks) c) What are the assumptions in derivation of continuity equation? (6 Marks) 2 m diameter 1 m diameter Q Q 5m Figure 11 8/-

8 - 8 - Rajah 1 1. a) Terangkan persamaan dan perbezaan dalam konsep Pengabadian Tenaga dalam Roller Coaster dan mekanik bendalir dari Rajah 1 berikut. (5 Markah) Rajah 2 b) Berpandukan Rajah 2, satu pancutan air dengan kadar alir Q = 0.12m 3 /s dan bergarispusat d=25mm menghentam sebuah plat pada sudut θ = 60 o. Cari nilai daya dan arahnya sekira: i) Plat berkedudukan statik ii) Plat bergerak dari pancutan tersebut dengan kelajuan 0.25 m/s (15 Markah) 9/-

9 - 9 - Rajah 3 2. a) Berdasarkan Rajah 3, bentukkan persamaan V B = 2gH dan nyatakan andaian. (3 markah) Rajah 4 b) Dalam kes Rajah 4, air mengalir dengan kadar alir sebanyak 0.2m 3 /s ke dalam tangki silinder yang bergarispusat 1m dan mengalir melalui paip sepanjang 4m dan bergarispusat 15sm. Cari nilai kedalam air dalam tangki silinder tersebut (H). (10 markah) 10/-

11 a) Berikan definasi bagi tekanan, ketumpatan, berat tentu, graviti tentu, kelikatan dinamik dan kelikatan kinematik. (4 markah) b) Batu mempunyai graviti tentu 2.32 dan isipadu 1.43x10-4 m 3. Berapakah berat batu tersebut. (6 markah) b) Terbitkan persamaan untuk perubahan ketinggian h untuk tiub yang mengandungi cecair dengan tegangan permukaan σ dan sudut θ seperti di Rajah 7. (10 markah) Rajah 7 12/-

12 a) Tentukan jumlah daya dan pusat tekanan untuk kes-kes tersebut : Water surface 0.5 m 0.5m 2 m 0.5 m 1 m 1 m 1 m 2 m 2 m Rajah 8 4 m (a) (b) (c) b) Tekanan tolok di B tentukan oleh tekanan di A. Sekiranya tekanan di B adalah 87 kpa, berdasarkan Rajah 9 hitung tekanan di A. Andaian : (Suhu adalah 20 o C, berat tentu air adalah 9810 N/m 3, berat tentu raksa N/m 3 buat tentu minyak 8720 = N/m 3 ). Gauge B - ooo O ooo - Rajah 9 13/-

13 a) Sebuah blok konkrit mempunyai berat 100N dan berat di dalam air adalah 60N ketika terendam (1000N/m 3 ). Cari nilai purata berat tentu bagi blok tersebut. 60N F B W = 100N Rajah 10 b) Sebatang paip bertukar diameter 1 m ke 2 m bagi jarak 5 meter. Sekiranya kadar alir Q (m 3 /s) mengalir dari keratan rentas 1 m ke keratan rentas 2 m, terbitkan persamaan halaju. Sila rujuk pada Rajah 11. (8 marks) b) Apakah andaian-andaian dalam penerbitan persamaan keselanjaran? (6 markah) 2 m diameter 1 m diameter Q Q 5m Rajah 11 14/-

14 Appendix 1/ Lampiran Relationship between Drag coefficient, C D and Reynold number, N R 15/-

15 Appendix 2/ Lampiran 2 Temperature, density, specific heat, thermal conductivity, expansion coefficient, kinematic viscosity and Prandtl's number for temperatures ranging o C Sponsored Links Temperature - t - ( o C) Density - ρ - (kg/m 3 ) Specific heat capacity - c p - (kj/kg K) Thermal conductivity - l - (W/m K) Kinematic viscosity - ν - (m 2 /s) x 10-6 Expansion coefficient - b - (1/K) x 10-3 Prandtl's number - P r ooooooo-

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