= Prismatic triangular-channel shallow water equations
For fixed channel width $b(z)=\beta z$, cross-sectional area is $A=\beta h^2/2$. With <reduced gravity> $G\phi$, uniform cross-sectional fields and downward <settling velocity> magnitude $w$, <volume conservation>, <momentum> and <particle deposition flux> give
$$
h_t+uh_x+(h/2)u_x=0,\qquad u_t+uu_x+G\phi h_x+(Gh/3)\phi_x=0,\qquad\phi_t+u\phi_x=-2w\phi/h.
$$
The <hydrostatic pressure> force contains $\int_0^h(h-z)\beta z\,dz=\beta h^3/6$. No streamwise widening term occurs in a prismatic channel. Deposition uses the projected boundary width $\beta h$ under the vertical-settling model.
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