Poiseuille flow Boundary conditions r = a u = U r = b u = 0 circular pipe. a.) find velocity profile b.) find Drag. c.) find pressure gradient which makes Drag zero.
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In regions far from the entrance, fluid flow through a circular pipe is one-dimensional, and the velocity profile for laminar flow is given by u(r) = umax(1 - r^2/R^2), where R is the radius of the pipe, r is the radial distance from the center of the pipe, and umax is the maximum flow velocity, which occurs at the center. Obtain (a) a relation for the drag force applied by the fluid on a section of the pipe of length L and (b) the value of the drag force for water flow at 20°C with R = 0.08 m, L = 30 m, umax = 3 m/s, and μ = 0.0010 kg/m·s.
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For low-speed (laminar) steady flow through a circular pipe, as shown in Fig. P1.12, the velocity $u$ varies with radius and takes the form $$u=B \frac{\Delta p}{\mu}\left(r_{0}^{2}-r^{2}\right)$$ where $\mu$ is the fluid viscosity and $\Delta p$ is the pressure drop from entrance to exit. What are the dimensions of the constant $B ?$
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