Sprinkler & fire pump hydraulics (NFPA 13/20)

modified2026-07-21statusfinished

NFPA 13/20 water-based fire suppression hydraulics — sprinkler discharge, pipe friction loss, fitting equivalents, hazard demand, and fire pump NPSH, in one reference.

Index

Sprinkler discharge & K-factor
Hazen-Williams friction loss
Equivalent pipe length
Sprinkler density/area demand
Fire pump net head & NPSH

Each relation set below includes a Voici¹1Voici compiles a notebook to a static, serverless dashboard — mocked here as a static page, since this pipeline has no Jupyter kernel to run against. dashboard: a matplotlib-styled chart with the live calculator input marked as a red point on the curve.

1.7 · Sprinkler discharge & K-factor

[1.7] Governing equation

$$Q = K\sqrt{P}$$

$K$ orifice discharge coefficient (gpm/psi^0.5), $P$ pressure at the sprinkler (psi). Source: NFPA 13 §27.2.

FIG. 01 — pendent sprinkler: orifice K-factor sizes the discharge cone from supply pressure P

K-factor (gpm/psi^0.5) Pressure P (psi)

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import numpy as np, matplotlib.pyplot as plt
P = np.linspace(1, 100, 200)
Q = K*np.sqrt(P)
plt.plot(P, Q); plt.scatter([P_input],[Q_input], color='red', zorder=3)

FIG. 02 — discharge Q vs. pressure P, current P marked in red

1.8 · Hazen-Williams friction loss

[1.8] Governing equation

$$p_m = 4.52\,\frac{Q^{1.85}}{C^{1.85}\,d^{4.87}}$$

$Q$ flow (gpm), $C$ pipe roughness factor (120 black steel typical), $d$ internal diameter (in). Source: NFPA 13 §27.2, NFPA 14.

FIG. 03 — friction loss slopes the hydraulic grade line down along the pipe run

Flow Q (gpm) C-factor Internal diameter d (in)

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import numpy as np, matplotlib.pyplot as plt
Q = np.linspace(5, 300, 200)
pm = 4.52*Q**1.85/(C**1.85*d**4.87)
plt.plot(Q, pm); plt.scatter([Q_input],[pm_input], color='red', zorder=3)

FIG. 04 — friction loss pm vs. flow Q, current Q marked in red

1.9 · Equivalent pipe length

[1.9] Governing relation

$$L_{eq} = \sum n_i L_{i,\text{table}}$$

Converts fittings to equivalent straight pipe length (Schedule 40 steel, typical NFPA 13 Table 27.2.3.1.1 values). Source: NFPA 13 Table 27.2.3.1.1.

FIG. 05 — common fittings, each replaced by an equivalent length of straight pipe

Fitting type Nominal pipe size (in) Quantity

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1.10 · Sprinkler density/area demand

[1.10] Governing equation

$$Q_{\text{demand}} = \left(\text{Density}\times\text{Design Area}\right) + Q_{\text{hose}}$$

Baseline water supply demand by hazard classification. Source: NFPA 13 §19.3.

FIG. 06 — hazard density applied over the hydraulically most demanding design area, plus hose stream allowance

Hazard preset Density (gpm/ft²) Design area (ft²) Hose stream allowance (gpm)

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import numpy as np, matplotlib.pyplot as plt
area = np.linspace(500, 5000, 200)
Q = density*area + Qhose
plt.plot(area, Q); plt.scatter([area_input],[Q_input], color='red', zorder=3)

FIG. 07 — total demand Q vs. design area, current area marked in red

1.11 · Fire pump net head & NPSH

[1.11] Governing equation

$$\text{NPSHA} = h_{sa} + h_s - h_{fs} - h_{vp}$$

$h_{sa}$ atmospheric pressure head (33.9 ft at sea level), $h_s$ static suction head (negative if a lift), $h_{fs}$ suction friction loss, $h_{vp}$ vapor pressure head. Source: NFPA 20 §4.15.

FIG. 08 — suction lift, friction loss, and vapor pressure combine to set NPSH available at the pump flange

Atmospheric head hsa (ft) Static suction head hs (ft, negative if lift) Suction friction loss hfs (ft) Vapor pressure head hvp (ft) Required NPSHR (ft, from pump curve)

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import numpy as np, matplotlib.pyplot as plt
hs = np.linspace(-20, 20, 200)
NPSHA = hsa + hs - hfs - hvp
plt.plot(hs, NPSHA); plt.axhline(NPSHR, ls='--'); plt.scatter([hs_input],[NPSHA_input], color='red', zorder=3)

FIG. 09 — NPSHA vs. static suction head hs, current hs marked in red (dashed line: required NPSHR)