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HW #4 Hand-out Solutions
4.
(P1/
g ) + (v12 / 2g)+ z1 = (P2 / g )+ (v22 / 2g)+ z20 + 0 + z1 = 0 + (v22 / 2g)+ z2
v22 = 2 g * (z1 - z2 )
v22 = 2 * 9.81 m/s2 * (0.7 m – 0.1 m)
v22 = 11.7 m2/s2
v2 = 3.4 m/s
5.
(P1/
g ) + (v12 / 2g)+ z1 = (P2 / g )+ (v22 / 2g)+ z2(P1/
g ) + (v12 / 2g)+ 0 = 0 + (v22 / 2g)+ 0
Q1 = Q2
A1v1 = A2v2
V2 = (A1v1)/A2
A1 =
P * (0.05 ) 2 = 0.0078 m2A2 =
P * (0.025 ) 2 = 0.00196 m2[2 * g * (7,500 N/m2 / 9810 N/m3)] + v12 = ((A1v1)/A2) 2
[2 * g * (7,500 N/m2 / 9810 N/m3)] + v12 = (15.8) v12
[2 * g * (7,500 N/m2 / 9810 N/m3)] = 14.8 v12
14.89 m2 /s2 = 14.8 v12
v1 = 1 m/s
6.
Q = 2 * 104 m3/s V = Q/A = (2 * 104 m3/s) / (3.14 * 10 –4 m2) = 0.64 m/s
D = 0.02 m A =
P * (0.01 m) 2 = 3.14 * 10 –4 m2m
= 1 * 10 –3 Ns/m2r
= 1000 kg/m3
A.
R = (v D
r ) / m = [(0.64 m/s) (0.02 m) (1000 kg/m3)] / (0.001 Ns/m2)= R = 12,800 , flow is turbulent
B.
f = 0.316 / (R1/4 )= 0.316 / (28,000 1/4 ) = f = 0.0298
Hf /L = (f /D) ( v2 / 2g)= [(0.0298) (0.64m/s)2] / [(0.02 m) (19.6 m/s2)] = hf /L= 0.03
C.
(P1/
g ) + (v12 / 2g)+ z1 = (P2 / g )+ (v22 / 2g)+ z2
(P1/
g ) + 0 + 0 –hf = 0 + 0 + 0
P1 =
g * hfP1 = (9810 N/m3 ) (0.03) (10 m)
P1 = 2.94 KPa
7.
D = 1 m A =
P * (1 m) 2 = 3.14 m2m
= 1 * 10 3 Pa sr
= 2700 kg/m3
(P1/
g ) + (v12 / 2g)+ z1 = (P2 / g )+ (v22 / 2g)+ z20 + (v12 / 2g) + 0 = (P2 /
g )+ 0 + 0(v12 / 2g) = (P2 /
g )v12 = (2g /
g ) P2v12 = (2 / 2700 kg/m3 ) * 2000 Pa
v12 = 1.5 m2/s2
v1 = 1.2 m/s
Q = vA = (1.2 m/s) * (3.14 m2) = Q = 3.8 m3/s
R = (v D
r ) / m = [(1.2 m/s) (1 m) (2700 kg/m3)] / (103 N s/m2)= R = 3.2 assumption is valid