Question

So I've been given the following values from an experiment where we ran water through a pipe and were told to observe only the Q(gpm) and the change in Pressure(psi). From there, we need to calculate the head loss, s-value, f-value, and the Hazen-Williams coefficient. So I need help figuring out which equations to use for those?

Answer 1

Ans) According to question , flow rate (Q) and change in pressure ($\dpi{100} \Delta$P) are known and we need to determine head loss , slope Darcy friction factor (f) and Hazen-William coefficient (C) .

Apply Bernoulli equation between between any two point inside pipe ,

P1 / $\dpi{100} \gamma$ + V1² / 2g + Z1 = P2 / $\dpi{100} \gamma$ + V2² / 2g + Z2 + H_L

=> H_L = $\dpi{100} \Delta$ P/$\dpi{100} \gamma$ + (V1² - V2²) / 2g + $\dpi{100} \Delta$ Z

Velocity can be determined by using Q = A x V , where A is cross sectional area of pipe = ($\dpi{100} \pi$/4) D²

From above equation , head loss can be determined

Also, using equation H_L = f L V² / ( 2 g D) , we can determine Darcy friction factor (f) = 2 g D H_L / L V²

Also, H_L = 10.67 L Q^1.85 / C^1.85 D^4.87

where, C = Hazen William coefficient (C)

Using above equation, we can determine Hazen William coefficient (C) ,

Now, slope (s) can be determined using below equation,

V = k C R^0.63 s^0.54

where, k = conversion factor = 1.318 for US unit and 0.849 for SI unit

R = Hydraulic depth = D/ 4 ,where D is diameter of pipe