Question

Newtonian fluid with a viscosity of 10 cP is placed between two large parallel plates. The distance between the plates is 4 mm. The lower plate is pulled in the positive x-direction with a force of 0.5 N. Each plate has an area of 2.5 m2. a. If the top plate is stationary, calculate the velocity of the lower plate.b. If the upper plate is pulled in the negative x-direction with a force of 2 N and the velocity of the lower plate is 0.1 m/s, calculate the velocity of the upper plate​

Answer 1

Answer:

A Newtonian fluid with a viscosity of 10 cP is placed between two large parallel plates. The distance between the plates is 4 mm. The lower plate is pulled in the positive x-direction with a force of 0.5 N, while the upper plate is pulled in the negative x-direction with a force of 2 N. Each plate has an area of 2.5 m2. If the velocity of the lower plate is 0.1 m/s, calculate:

a) The steady-state momentum flux,

b) The velocity of the upper plate.

Answer 2

Answer:

(a) The steady-state momentum flux is 1 Pa.

(b) The velocity of the upper plate is -0.03 m/s.

Step-by-step explanation:

(a) The momentum flux 0r force per unit area is:

$T_{yx}$

$T_{yx} = \frac{F}{A} = \frac{0.5+2}{2.5}$

Thus, The steady-state momentum flux is 1 Pa.

(b) Let, $V_{2}$, be the velocity of the upper plate.

Therefore, $T_{yx} \int\limits^Y_o {} \, dy = -\alpha \int\limits^V_{2} _V_{1} {} \, dv_{x}$

$V_{2}=V_{1} - \frac{T_{yx}Y }{\alpha }$ ..............(1)

SUbstitutuign vales,

$V_{2} = 0.1 - \frac{(1)(4*10^{-3}) }{10*10^{-3} } = 0.03 m/s$

The lower plate travels in the negative x-direction, as shown by the minus symbol. The velocity gradient is, as you can see, -100$s^{-1}$

Newtonian fluid:

• A Newtonian fluid is one in which the local strain rate, or the rate of change of its deformation over time, is linearly connected to the viscous stresses resulting from its flow at every place.
• The rate at which the fluid's velocity vector changes determines how much stress is there.
• Only when the tensors describing the viscous stress and strain rate are coupled by a constant viscosity tensor that is independent of the stress state and flow velocity can a fluid be said to be Newtonian.

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