In regions far from the entrance, fluid flow througha circular pipe is one dimensional, and the velocity profile forlaminar flow is given by u(r) = umax(1 - r 2/R2), where R isthe radius of the pipe, r is the radial distance from the center ofthe pipe, and umax is the maximum flow velocity, which occursat the center. Obtain (a) a relation for the drag force applied bythe fluid on a section of the pipe of length L and (b) the valueof the drag force for water flow at 20°C with R 5 0.08 m,L = 30 m, umax = 3 m/s, and m = 0.0010 kg/m?s.
Fluid Pressure
The term fluid pressure is coined as, the measurement of the force per unit area of a given surface of a closed container. It is a branch of physics that helps to study the properties of fluid under various conditions of force.
Gauge Pressure
Pressure is the physical force acting per unit area on a body; the applied force is perpendicular to the surface of the object per unit area. The air around us at sea level exerts a pressure (atmospheric pressure) of about 14.7 psi but this doesn’t seem to bother anyone as the bodily fluids are constantly pushing outwards with the same force but if one swims down into the ocean a few feet below the surface one can notice the difference, there is increased pressure on the eardrum, this is due to an increase in hydrostatic pressure.
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/R2), 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 5 0.08 m,
L = 30 m, umax = 3 m/s, and m = 0.0010 kg/m?s.
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