The viscosity of a fluid, denoted by u, is a measure of the fluid's resistance to deformation or flow and has dimension ML-¹T-¹ (i.e. [u] = ML-¹T-¹). Suppose a sphere of radius r falls and moves through a fluid with a speed v and experiences a drag force F. olmios Suppose the drag force F depends only on v, μ, and r. Show that the only dimensionally consistent formula for F in terms of these variables is given by F = kruv, where k is a dimensionless constant.
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.
Write on paper
![The viscosity of a fluid, denoted by \(\mu\), is a measure of the fluid’s resistance to deformation or flow and has dimensions \([ML^{-1}T^{-1}]\) (i.e., \([\mu] = ML^{-1}T^{-1}]\). Suppose a sphere of radius \(r\) falls and moves through a fluid with a speed \(v\) and experiences a drag force \(F\).
Suppose the drag force \(F\) depends only on \(v\), \(\mu\), and \(r\). Show that the only dimensionally consistent formula for \(F\) in terms of these variables is given by \(F = k\mu vr\), where \(k\) is a dimensionless constant.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F590efbb4-bfa3-48e4-b7a4-ba8d0f00ec23%2F724452eb-8a32-40d0-80c1-820047edcbd8%2Fl1bw22_processed.jpeg&w=3840&q=75)
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
