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Table of equations, mainly for rivers.

Basic
Force balance	SF = 0, or  SF = ma	The second form is used if there are any accelerations
Hydro or litho static pressure	P = r g d	r is the material density, and d is the depth of burial
Shear and normal stress in a fluid
Shear stress, parallel to slope at some depth (depth perpendicular to slope, but often just the vertical depth is used.)	t = rgd sina	See notes on slope angles and depths
Normal stress, perpendicular to slope	s = rgd cosa
Reynolds number	Re = r v d / m	Where v is a flow direction velocity and d is a cross stream dimension
Froude number	Fr = v / ( g d )^1/2
Stoke’s setting velocity	w = (rs - rf) g D^2 / ( 18 m )
Shear velocity	U* = ( tb / rf)^1/2
Bernoulli pressure/velocity	DPw = - (Dv)^2 /2
Shield’s parameter	Q = tb / (rs - rf) g D	This equation can be inverted to get the critical shear stress tc to get a particle moving
Mannings equation	V = R^2/3 S^1/2 / n	R is the cross-section area divided by the wetted perimeter, S is slope and n is tabulated, this equation is written for MKS units only
Chezy eqn.	V = C R^1/2 S^1/2
MPM equation for sediment load	qs = A (tb - tc) 3/2	Bedload or total load per unit width of channel
Super-elevation in meander bends	Dz = v^2 w / (gR)	W is the channel width, and R is the bend radius
Alluvial diffusion equation		If the second term is ignored, this is just the simple diffusion equation, and can be thought of in terms of behavior just like the rainsplash equation
Bedrock kinematic equation		This is a kinematic wave equation with velocity Eqw.