4 Two sections A and B are 45 km apart along a 4m diameter r

4. Two sections, A and B are 4.5 km apart along a 4-m diameter riveted-steel pipe in its best condition. A is 100 m higher than B. if the water temperature is 20°C and the pressure heads measured at A and B are 8.3 m and 76.7 m, respectively, what is the flow rate?

Solution

Solution:-

L = 4.5 km = 4500 m

D = 4 m

z_A = 100 m

z_B = 0

p_A/y = 8.3 m

p_B/y = 76.7 m

V_A²/2g + p_A/y + z_A = V_B²/2g + p_B/y + z_B + h_L

h_L = f LV²/(2gD)

   V_A = V_B

p_A/y + z_A = p_B/y + fLV²/(2gD)

V = (2gD/(f L)*(p_A/y + z_A – p_B/y))

f = 0.0015

V = (2*9.81*4/(0.015*4500)*(8.3 + 100 – 76.7))

V = 6.061 m/s

Q = A*V

Q = /4*D² * V

Q = /4 * (4)² * 6.061

Q = 76.164 m³/s   Answer