HW #4 Hand-out Solutions

4.

(P1/ g ) + (v12 / 2g)+ z1 = (P2 / g )+ (v22 / 2g)+ z2

0 + 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 m2

A2 = 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 m2

m = 1 * 10 –3 Ns/m2

r = 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 * hf

P1 = (9810 N/m3 ) (0.03) (10 m)

P1 = 2.94 KPa

 

 

7.

D = 1 m A = P * (1 m) 2 = 3.14 m2

m = 1 * 10 3 Pa s

r = 2700 kg/m3

 

(P1/ g ) + (v12 / 2g)+ z1 = (P2 / g )+ (v22 / 2g)+ z2

0 + (v12 / 2g) + 0 = (P2 / g )+ 0 + 0

(v12 / 2g) = (P2 / g )

v12 = (2g / g ) P2

v12 = (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