Anewtonian fluid is placed in a slit of thickness, h, between two flat, plates that are horizontal to gravity. the upper plate moves at velocity u parallel to the lower plate, which is stationary. find the velocity profile in the slit.

Proof with Explanation:

From the Newton's law of viscosity we have

where is the wall shear stress

is the coefficient of dynamic viscosity

is the velocity gradient in the flow

Now from the principle of boundary layer condition we know that the velocity of the fluid that is in contact with a surface the velocity of the fluid is same as that of the boundary itself.

Hence from the attached figure we can infer that

Velocity at

Velocity at

Solving equation 'i' we get

from the boundary conditions we obtain that c = 0 since

Also we have

sleep paralysis is a parasomnia, events associated with sleep.

sleep paralysis happens when you are in the middle of waking up or falling asleep. it is the feeling of being conscious but unable to move. it definitely involves hallucinations.

i had a friend that had sleep paralysis and he told me a story one time where he was laying in bed and he couldn't move his body no matter how hard he tried and there was someone standing in the corner of his room coming towards him. he couldn't move and you can't "wake up" because you are already conscious. sometimes sleep paralysis can be triggered by frequent waking up during the night based off of multiple trips to the bathroom, or if you had ever been abused, sleep paralysis can start happening from things like that.