Video Transcript
Fill in the blank. Two flat plates have a liquid between them. If the tangential force applied to the top plate is halved, then the coefficient of
viscosity of the liquid between the plates blank. (A) Decreases to half, (B) doubles, (C) decreases to quarter, (D) is not
affected.
Let’s look at a diagram showing the two plates and the layers of fluid between
them. From our question statement, we understand that a tangential force, we’ll call it 𝐹,
is acting on the top plate. We could assume the bottom plate has no force acting on it, so the layers of fluid
will move at different speeds. These speeds depend on the viscosity coefficient of the liquid. The lower this value, the more easily layers of liquid will slide past one
another. Fluid viscosity, represented by the Greek letter 𝜇, is given by this
relationship. Here, 𝐹 is the tangential force. 𝐴 is the area of the plate in contact with the fluid. And Δ𝑦 is the perpendicular distance from the plate over which the fluid’s speed in
the 𝑥-direction changes by the quantity Δ𝑣 sub 𝑥.
We are asked how reducing 𝐹 by half will affect 𝜇. The magnitude of 𝐹 affects the slope of the line Δ𝑦 over Δ𝑣 sub 𝑥. The smaller the force, the less 𝑣 sub 𝑥 will change for a given distance from the
plate. In fact, for a given fluid and distance from the plate, halving the force 𝐹 will
reduce the change in fluid velocity Δ𝑣 sub 𝑥 by half. In other words, when 𝐹 is reduced to 𝐹 over two, Δ𝑣 sub 𝑥 is reduced to Δ𝑣 sub
𝑥 over two.
Let’s substitute these new values into the equation for fluid viscosity. Notice that a factor of one-half appears in numerator and denominator, so we can
cancel this out. We find that the viscosity remains unchanged. This makes sense because changing the force we apply to a fluid doesn’t change any
basic properties of that fluid. It still has the same viscosity coefficient as before.
So, the correct answer is option (D). Filling in our blank, our completed sentence reads “If the tangential force applied
to the top plate is halved, then the coefficient of viscosity of the liquid between
the plates is not affected.”
