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sm_ch02

Water Resources Engineering

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2 – 1 Chapter 2 2.1.1. V = 10 m 3 , W = 60 kN. Specific weight, J = W/V = 60 kN/10 m 3 = 6 kN/m 3 = 6000 N/m 3 Density, U = J /g = 6000 N/m 3 /9.81 kN/m 3 = 611.62 kg/m 3 Specific gravity, s.g. = J / J w = 6 kN/m 3 /9.81 kN/m 3 = 0.612. 2.1.2. s.g. = 0.7. In SI units: U oil = s.g. U w = 0.7(1000 kg/m 3 ) = 700 kg/m 3 . J oil = s.g. J w = 0.7(9810 N/m 3 ) = 6867 N/m 3 . In English (FPS) units: U oil = 0.7(1.94 slugs/ft 3 ) = 1.36 slugs/ft 3 . J oil = 0.7(62.4 lb/ft 3 ) = 43.68 lb/ft 3 . 2.1.3. From Newton’s second law, F = ma. Thus, unit of force = unit of mass x unit of acceleration = kg x m/s 2 . This is unit is called newton, denoted by N, and it is equivalent to kg x m/s 2 . 2.1.4. In English units, unit of mass = the unit of Force divided by the unit of acceleration due to gravity = lb/(ft/s 2 ) = lb-s 2 /ft. This unit is called slug, and it is thus equivalent to lb-s 2 /ft. 2.1.5. W earth = 9810 N. g moon = (1/6)g earth = (1/6)(9.81 m/s 2 ) = 1.635 m/s 2 . M earth = M moon = W earth /g earth = 9810 N/9.81 m/s 2 = 100 kg. W moon = M moon g moon = 100 kg (1.635 m/s 2 ) = 163.5 N. 2.1.6. T = 110 o F. Using the relationship o C = (5/9)( o F – 32): T in o C = (5/9)(110 – 32) = 43.33 o C. 2.1.7. At 20 o C, 50 o C and 80 o C, the densities of water are 998.2 kg/m 3 , 988.1 kg/m 3 and 971.8 kg/m 3 , respectively (Table 2.1.2). Thus, from (i) 20 o C to 50 o C, percent change in U = (998.2 – 988.1)(100)/998.2 = 1 %; (ii) 20 o C to 80 o C percent change in U = (998.2 – 971.8)(100)/998.2 = 2.6%. 2.2.1. Q = 4 x 10 -4 m 2 /s, s.g. = 1.5. U liquid = s.g. U w = 1.5(1000 kg/m 3 ) = 1500 kg/m 3 . P = QU = 4 x 10 -4 (1500 kg/m 3 ) = 0.6 N-s/m 2 (Pa-s) 2.2.2. P = 2.09 x 10 -5 lb-s/ft 2 . In N-s/m 2 , m = [2.09 x 10 -5 lb-s/ft 2 ] x [4.448 N/lb] x [1 ft/0.3048 m] 2 = 1x 10 -3 N-s/m 2 (kg/m.s) 1 poise = 1 g/cm.s, and 1 centipoise = 0.01 g/cm.s = 0.001 kg/m.s. Thus, 2.09 x 10 -5 lb-s/ft 2 = 1 centipoise. 2.2.3. 1 stoke = 1 cm 2 /s = 10 -4 m 2 /s.
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2 – 2 1 centistoke = 0.01 stoke = 10 -6 m 2 /s. Thus, 800 centistokes = 800 x 10 -6 m 2 /s = 8 x 10 -4 m 2 /s.
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sm_ch02 - 21 Chapter 2 2.1.1 V = 10 m3 W = 60 kN Specific...

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