# Flow Rate

Written by Jerry Ratzlaff on . Posted in Fluid Dynamics

Flow rate, abbreviated as Q, also called volumetric flow rate, measure the amount of fluid that flows in a given time past a specific point if the temperature and pressure were at standard conditions.

## Flow Rate formula

$$\large{ Q = A_c \; v }$$

$$\large{ Q = C_v \; \sqrt {\frac{SG} {\Delta p} } }$$

$$\large{ Q = k \; i \; A_c }$$

$$\large{ Q = \frac{ 1.49 }{ n } \; A_c \; r_h^{2/3} \; S^{1/2} }$$

$$\large{ Q = \frac{ 3960 \; WHP }{ h_t } }$$

Symbol English Metric
$$\large{ Q }$$ = flow rate $$\large{\frac{ft^3}{sec}}$$ $$\large{\frac{m^3}{s}}$$
$$\large{ A_c }$$ = area cross-section $$\large{ft^2}$$ $$\large{m^2}$$
$$\large{ S }$$ = channel slope or energy slope line  $$\large{ft}$$  $$\large{m}$$
$$\large{ C_v }$$ = flow coefficient $$\large{dimensionless}$$
$$\large{ k }$$ = hydraulic conductivity  $$\large{\frac{ft}{day}}$$  $$\large{\frac{m}{day}}$$
$$\large{ i }$$ = hydraulic gradient $$\large{dimensionless}$$
$$\large{ r_h }$$ = hydraulic radius $$\large{ft}$$ $$\large{m}$$
$$\large{ \Delta p }$$ = pressure differential $$\large{\frac{lbf}{in^2}}$$   $$\large{Pa}$$
$$\large{ SG }$$ = specific gravity of fluid (water at 60°F = 1.0000)  $$\large{\frac{ft}{sec^2}}$$    $$\large{\frac{m}{s^2}}$$
$$\large{ h_t }$$ = total head or height $$\large{ft}$$ $$\large{m}$$
$$\large{ v }$$ = velocity $$\large{\frac{ft}{sec}}$$ $$\large{\frac{m}{s}}$$
$$\large{ WHP }$$ = water horsepower  $$\large{\frac{lbf-ft}{sec}}$$ $$\large{\frac{Btu}{s}}$$