Mechanical Properties of Fluids Test - 11

Torricelli's law states that the speed of efflux $$v$$ of a fluid through a sharp-edged hole at the bottom of a tank filled to a depth $$h$$ is the same as the speed that a body would acquire in falling freely from a height $$h$$, i.e. $$v=\sqrt{2gh}$$

Gravity does cause things to fall with increasing speed, but as they speed up viscous force due to air increases. Eventually the viscous force due to air is enough to balance the force of gravity, so the acceleration stops and the raindrop reaches a constant terminal velocity.

Terminal velocity is said to be achieved when the body has attained equilibrium under gravity, buoyant and viscous forces, and velocity no more changes due to any acceleration.Here velocity is constant so accceleration of sphere is zero .

By definition, In streamline flow the velocity of flow at any chosen point in the liquid is always the same i.e. doesn't vary with time.

According to Torricelli's Theorem velocity of efflux i.e. the velocity with which the liquid flows out of a hole is equal to $$\sqrt{2gh}$$ where $$h$$ is the depth of the hole below the liquid surface. Hence more the depth of the hole, more will be the velocity of the liquid coming out of the hole, and will be maximum if the hole is at bottom of the tank.

Concave shape is the correct answer.
Water is made up of polar molecules, which have positively and negatively charged ends. Since opposites attract, the positive sides attract the negative sides, and all of the molecules stick to one another. This is why water droplets can form. Glass molecules also happen to be polar. Again, since polar molecules like to stick together, the water in a glass tube will actually tend to stick to the sides of the tube! You can see this at the top of the graduated cylinder, where the water will slightly creep up the sides and form a curve, which is the meniscus.

(a) What do you understand by the term meniscus?
The meniscus (plural: menisci, from the Greek for "crescent") is the curve in the upper surface of a liquid close to the surface of the container or another object, caused by surface tension. It can be either convex or concave, depending on the liquid and the surface.
(b) Name the kind of meniscus formed
(i) in case of water
Concave meniscus is formed. Water is made up of polar molecules, which have positively and negatively charged ends. Since opposites attract, the positive sides attract the negative sides, and all of the molecules stick to one another. This is why water droplets can form. Glass molecules also happen to be polar. Again, since polar molecules like to stick together, the water in a glass tube will actually tend to stick to the sides of the tube. You can see this at the top of the graduated cylinder, where the water will slightly creep up the sides and form a curve, which is the meniscus.
(ii) in case of mercury
Convex meniscus is formed. The reason for this happening is because of cohesion and adhesion. Meniscus is the curve of the upper surface in any liquid. It can be convex with is the curving outward or bulge outward. Concave is just the opposite. 

The expression for the capillary rise in a tube is given by, 

H = $$ \dfrac {2T cos \theta}{\rho gr} $$

where $$ \theta$$ is the contact angle and not the angle of tilt.

Thus, for all parameters constant,

at $$ 60^o $$

$$ l_1 = H cos 60^0 $$ = H/2

At $$ 45^o $$

$$ l_2 = H cos 45^0 $$ = $$ H/\sqrt 2 $$

Therefore the ratio of the 2 lengths is given by,

$$ l_1/l_2 = \dfrac {1}{\sqrt 2} $$

As a result of coating the insides of a capillary tube with wax, the forces within the water molecules tend to become stronger than that of water with the wax. As a result, water loses its ability to wet the sides of the tube and therefore cannot creep up the walls. Therefore, it tends to depress its level to as a result of forces of surface tension acting in the downward direction along with the weight of water. 

Meniscus (plural - menisci) from greek "crescent" is corve in the upper surface of a liquid close to the surface if the container or another object caused by surface tension.