Water can be a force of Immense Devastation
 Fluid Dynamics

### Continuity Equation

The continuity equation states that the mass flow rate is constant at steady state:

\dot{m} = \rho_1A_1 V_1 = \rho_2 A_2 V_2 = constant

where:

ρ = mass density (slugs/ft3)
A = cross-sectional area of the flow(ft2)
V = velocity of the flow (ft/sec)

Because liquids can be assumed to have constant density over fairly large vertical distances, the continuity equation simplifies to:

Q = A_1V_1 = A_2V_2 = AV

where:

Q = discharge (ft3/sec)
A = cross-sectional area of the flow (ft2)
V = velocity of the flow (ft/sec)

### Energy Equation

The energy equation requires that the energy between two points may change form but the total is always conserved (See Bernoulli's Equation for more information):

EnergyInFluild_1 + EnergyAdded_{1\rightarrow2} = EnergyInFluid_2 + EnergyLost_{1\rightarrow2}

or...

\frac{P_1}{\gamma} + \frac{v_1^2}{2g} + Z_1 + I_1 +e_h + e_m = \frac{P_2}{\gamma} + \frac{v_2^2}{2g} + Z_2 + I_2 + h_L

The energy in the fluid at point 1 and 2 is the total of pressure, kinetic, potential, and internal energy. The energy added from point 1 to 2 is heat and mechanical energy. The energy lost from point 1 to 2 is called "head loss" (hL).

The energy equation is simplified in the case of fluids where the temperature doesn't change (I1 = I2) , no heat is added (eh = 0), and the only mechanical energy added is by a pump (em is replaced with hp):

\frac{P_1}{\gamma} + \frac{v_1^2}{2g} + Z_1 + h_P = \frac{P_2}{\gamma} + \frac{v_2^2}{2g} + Z_2 + h_L

where:

hp = head of the pump (ft)