# Eckert Number

on . Posted in Dimensionless Numbers

Eckert number, abbreviated as Ec, a dimensionless number, is used in thermodynamics and fluid dynamics to characterize the ratio of kinetic energy to thermal energy in a fluid flow.  It is defined as the ratio of the kinetic energy per unit mass to the specific enthalpy increment per unit temperature difference.  It is used to study the behavior of high speed fluid flows, such as those found in supersonic aircraft or rocket engines.  A high Eckert number indicates that the flow is dominated by kinetic energy, while a low Eckert number indicates that the flow is dominated by thermal energy.

## Eckert Number formula

$$\large{ Ec = \frac{ U^2 }{ 2 \; c \; \Delta T } }$$

### Eckert Number - Solve for Ec

$$\large{ Ec = \frac{ U^2 }{ 2 \; c \; \Delta T } }$$

 characteristic flow velocity, U specific heat, c temperature change, ΔT

### Eckert Number - Solve for U

$$\large{ U = \sqrt{2 \; Ec \; c \; \Delta T} }$$

 Eckert number, Ec specific heat, c temperature change, ΔT

### Eckert Number - Solve for c

$$\large{ c = \frac{ U^2 }{ 2 \; Ec \; \Delta T } }$$

 characteristic flow velocity, U Eckert number, Ec temperature change, ΔT

### Eckert Number - Solve for ΔT

$$\large{ \Delta T = \frac{ U^2 }{ 2 \; Ec \; c } }$$

 characteristic flow velocity, U Eckert number, Ec specific heat, c

Symbol English Metric
$$\large{ Ec }$$ = Eckert number $$\large{dimensionless}$$
$$\large{ U }$$ = characteristic flow velocity $$\large{\frac{ft}{sec}}$$ $$\large{\frac{m}{s}}$$
$$\large{ c }$$ = specific heat $$\large{\frac{Btu}{lbm-F}}$$  $$\large{\frac{J}{kg-K}}$$
$$\large{ \Delta T }$$ = temperature change $$\large{F}$$ $$\large{K}$$

Tags: Energy Equations