Is NJDOT's method of calculating friction losses correct?

Question

I have been attempting to develop a spreadsheet to calculate the hydraulic grade line (HGL) of a pipe system generally using the criteria set forth by the New Jersey DOT (NJDOT). Their Roadway Design Manual (link) states that the velocity head should be calculated as:

$$v_{head}=\frac{v^2}{2g}$$

This calculated value is then used as a multiplier for losses in the system like structural losses, bend losses, and friction losses.

The manner by which friction losses are calculated are as follows:

$$H_f=\frac{29.14n^2}{R_h^{1.33}}*v_{head}$$

I noted that this calculation method resulted in very few losses and for some reason did not relate the losses to the length of the pipe in any way that I could see.

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While conducting research on this, I found a different equation in the Flowmaster program, which describes velocity head as being calculated as:

$$v_{head}=\frac{v^2}{2g}$$

This is the same as NJDOT's, but the velocity head simply becomes part of the output data, but doesn't seem to factor into calculating the the friction losses in the pipe, which I determined is calculated as follows:

$$L*\left(\frac{n*Q}{1.486*A*R_h^{2/3}}\right)^2$$

This calculation resulted in losses which directly correlated with the length of the pipe the flow was passing through and with consideration for how full the pipe actually was. Ultimately, this seemed to be 'more' correct.

Definitions are as follows if needed:

• n: Manning's coefficient
• v: Velocity
• g: Gravitational constant
• R_h: Hydraulic radius
• Q: Flow rate
• A: Area of flow
• L: Length of pipe

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My question is as follows, the NJDOT method does have other contributory elements for system losses that Flowmaster doesn't account for. Specifically, NJDOT's method includes losses associated with bends, entrance and exit losses, impacts from laterals, etc. But is their means for calculating friction losses in the pipe 'correct' given that it does not relate the losses to the length of the pipe? I found when calculating the friction losses in Excel, the NJDOT method resulted in very negligible losses.

Answer 1

You are correct, the NJDOT spreadsheet neglects the length parameter in calculating the friction headloss.

Both of the equations you've shown are based upon the Manning's equation for open-channel flow.

$$v = \frac{1.486}{n} * R^{2/3} * S^{1/2}$$

Where S represents the friction slope of the hydraulic grade line. $$S=\frac{H_f}{L}$$

Using $$v = \frac {Q} {A}$$ and solving for the head loss in feet, we get: $$H_f = L * \frac{n^2}{1.486^2*R_h^\frac{4}{3}} * \frac{Q^2}{A^2}$$

Substituting $$\frac{Q^2}{A^2} = v^2 = 2g*v_{head}$$

We get $$H_f = L * \frac{2g}{1.486^2}*\frac{n^2}{R_h^\frac{4}{3}}*v_{head}$$

Taking Earth's gravity at 32.174 $\frac{ft}{sec^2}$, we get $\frac{2*32.174}{1.486^2} = 29.14$.

The NJDOT equation neglects the length term.