Consider a rectangular channel with a width w and thickness b, where b w filled with...

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Consider a rectangular channel with a width w and thickness b, where b≤ w filled with a liquid that will, for this problem at least, eventually flow. The channel is oriented at an angle relative to vertical. Po 9 P1 W Channel Cross Section Figure 2: (a) What approximation can we make to reduce the problem to a 1D problem, i.e. a velocity profile that only depends on one direction? (b) Derive the differential equation for the shear stress in terms of the pressure change and gravity 2 (c) What boundary conditions are appropriate for solving the problem? (d) Calculate the pressure distribution in a stagnant fluid over the entire length of the channel. (c) What must be true about the pressures, Po and P₁, if the fluid is to flow downward? (d) Derive an equation for the velocity profile. Assume that the fluid is Newtonian (e) Where is the location and what is the value of the maximum velocity? (f) Calculate the average velocity. Consider a rectangular channel with a width w and thickness b, where b≤ w filled with a liquid that will, for this problem at least, eventually flow. The channel is oriented at an angle relative to vertical. Po 9 P1 W Channel Cross Section Figure 2: (a) What approximation can we make to reduce the problem to a 1D problem, i.e. a velocity profile that only depends on one direction? (b) Derive the differential equation for the shear stress in terms of the pressure change and gravity 2 (c) What boundary conditions are appropriate for solving the problem? (d) Calculate the pressure distribution in a stagnant fluid over the entire length of the channel. (c) What must be true about the pressures, Po and P₁, if the fluid is to flow downward? (d) Derive an equation for the velocity profile. Assume that the fluid is Newtonian (e) Where is the location and what is the value of the maximum velocity? (f) Calculate the average velocity.