- #1
Raul Trejo
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Homework Statement
Consider the flow of a fluid with viscosity μ through a circular pipe. The velocity profile in the pipe is given as U(r)=Umax(1-rn/Rn), where Umax is the maximum flow velocity which occurs at the center line; r is the radial distance from the centerline; and U(r) is the flow velocity at any position r. Develop a relation for the drag force exerted in the pipe wall by the fluid in the flow direction per unit length of pipe.
Problem Image:
Homework Equations
Shear stress: τ=μ(du/dy) where μ=Viscosity coefficient and (du/dy)=Velocity gradient. Units are (N/m2)
Shear Force: F=τA=μ(du/dy)A; where A=Area of contact. Units are in N.
The Attempt at a Solution
I can't seem to grasp the idea of drag force for this problem, this problem is from Cengel and Cimbala's Fluid Mechanics 1st Edition. Problem number is 2-44. The problem I'm having is that no where in the theoretical part of the chapter do they mention the relationship between drag force and shear force, are they the same? The most the chapter mentions is the following: "The force a flowing fluid exerts on a body in the flow direction is called the drag force, and the magnitude of this force depends, in part, on viscosity". The solution manual also states that du/dr is negative, but I can't understand why.
Solution Manual image: