Water is flowing on a horizontal fixed surface, such that its flow velocity varies with y (vertical direction) as v=k((2 y2/a2)-(y3/a3)) If coefficient of viscosity for water is h, what will be shear stress between layers of water at y =a.

Question

Water is flowing on a horizontal fixed surface, such that its flow velocity varies with y (vertical direction) as v=k((2 y2/a2)-(y3/a3)) If coefficient of viscosity for water is h, what will be shear stress between layers of water at y =a. (A) (η k/a) (B) (η /ka) (C) (η a/k) (D) None of these

Tardigrade Admin · Accepted Answer

Newton's law of viscosity, F=η A (d v/d y) Stress =(F/A)=η((d v/d y)) =η k((4 y/a2)-(3 y2/a3)) At y=a, stress =η k((4/a)-(3/a)) =(η k/a)

Q. Water is flowing on a horizontal fixed surface, such that its flow velocity varies with y (vertical direction) as $v = k (\frac{2 y ^{2}}{a ^{2}} - \frac{y ^{3}}{a ^{3}})$ If coefficient of viscosity for water is $h$ , what will be shear stress between layers of water at $y = a$ .

$\frac{η k}{a}$

$\frac{η}{ka}$

$\frac{η a}{k}$

None of these

Newton's law of viscosity, $F = η A \frac{d v}{d y}$
Stress $= \frac{F}{A} = η (\frac{d v}{d y})$
$= η k (\frac{4 y}{a ^{2}} - \frac{3 y ^{2}}{a ^{3}})$
At $y = a$ , stress $= η k (\frac{4}{a} - \frac{3}{a})$
$= \frac{η k}{a}$

Q. Water is flowing on a horizontal fixed surface, such that its flow velocity varies with y (vertical direction) as v=k(a22y2​−a3y3​) If coefficient of viscosity for water is h, what will be shear stress between layers of water at y=a.

aηk​

kaη​

kηa​