Hydrostatic Law MCQ Quiz in বাংলা - Objective Question with Answer for Hydrostatic Law - বিনামূল্যে ডাউনলোড করুন [PDF]

Explanation:

Pressure Head:

The ratio of pressure intensity at a point and the specific weight of the fluid at that point is called pressure head 

ressure head = \(\frac{p}{ρ{g}}\)

Hydraulic head/Piezometric head:

Hydraulic head or piezometric head is a specific measurement of liquid pressure above a vertical datum. It is usually measured.

The sum of the pressure head and datum is known theas piezometric head. It is given by:

\(\frac{p}{ρ{g}}+z\)

The total energy of a flowing fluid can be represented in terms of head, which is given by -

\(\frac{p}{ρ{g}}\;+\;\frac{V^2}{2g}\;+\;z\;\)

\(where\;\frac{p}{\rho{g}}=pressure\;head,\;\frac{V^2}{2g}=velocity\;head\;and\;z=datum\)

Explanation:

• According to Hydrostatic Law, the rate of increase of pressure in a vertical direction is equal to the weight density of the fluid at that point when the fluid is stationary.
• The pressure at any point in a fluid at rest is obtained by the Hydrostatic Law which states that the rate of increase of pressure in a vertically downward direction must be equal to the specific weight of the fluid at that point.

\(\frac{{dP}}{{dh}} = w\) for downward direction

\(\frac{{dP}}{{dh}} = - w\) in upward direction

Thus, The rate of increase of pressure in a vertically downward direction is equal to Specific weight

Explanation:

According to Hydrostatic Law, the rate of increase of pressure in a vertical direction is equal to weight density of the fluid at that point when the fluid is stationary.

The pressure at any point in a fluid at rest is obtained by the Hydrostatic Law which states that the rate of increase of pressure in a vertically downward direction must be equal to the specific weight of the fluid at that point.

\(\frac{{dP}}{{dh}} = w\) for downward direction

\(\frac{{dP}}{{dh}} = - w\) for upward direction

P = ωh

Hence, p ∝ h

Thus, pressure in a stationary water column increases with depth and varies linearly and does not depend upon viscosity. 

It indicates that a negative pressure gradient exists upward along any vertical.

Explanation:

Hydrostatic law:

In a static fluid, the pressure depends on the vertical depth from the surface and it is independent of its shape and size of the container.

The pressure at a point inside a liquid is given by,

P = ρ × g × h

Where, h = Vertical height of the fluid column, ρ = Density of the liquid and

g = Acceleration due to gravity (9.81 m/s²)

• According to Hydrostatic law, the pressure at a point depends upon vertical depth from the liquid surface and independent of the shape of the container in a static fluid.
• In the given containers A and B, the point P lie at the same depth d and pressure varies only in the vertical direction.
• Hence the pressure at point P is the same in both containers A and B irrespective of the shape.

Example:

Pressure in A, B, and C, h height bellow from the water surface is the same.

Concept:

The pressure acts on the piston is, P = FA

where, F = force acts on piston, A = cross-section ara of piston

Calculation:

Given:

A = 25 cm², k = 10⁵ N/m, x = 10 mm = 10 × 10^-3 m

Force on piston (spring)

F = kx = 10⁵ × 10 ×10^-3 = 1000 N

Now pressure force by piston = P × 25 × 10^-4

On equating

P × 25 × 10^-4 = 1000 N

\( \Rightarrow P = \frac{{1000}}{{25 × {{10}^4}}} = 40 × {10^4} = 4 × {10^4} = 4 × {10^5}Pa\)

Explanation:

Concept:

Hydrostatic Law: This law states that the rate of increase of pressure in the vertical direction is directly proportional to the weight density of fluid at that point.

\(\frac{dP}{dz}=\rho g\)

Note: 

• In a vertically downward direction, pressure variation is taken as positive.
• In a vertically upward direction, pressure variation is taken as negative.

Absolute pressure: It is the sum of atmospheric pressure and gauge pressure.

\(P_{abs}=P_{atm}+P_{gauge}=P_{atm}+\rho gh\)

Calculation:

Given:

h_X = 10 m, h_Y = 12 m

\(\rho_{X}=\rho_{Y}\)

So, \(P_{absX}=P_{atm}+\rho_{X}gh_{X}=P_{atm}+\rho_{X}g(10)\)

similarly, \(P_{absY}=P_{atm}+\rho_{Y}g(12)\) 

The absolute pressure depends upon the distance of the point from the free surface.

\(\therefore\) \(P_{absY}>P_{absX}\) 

Thus, option (1) is correct answer.

CONCEPT:

• According to Blaise Pascal, a French scientist observed that the pressure in a fluid at rest is the same at all points if they are at the same height and it is termed Pascal’s Law.

• i.e., the pressure exerted by the fluid on an object at a certain height will be the same in all directions.

and hence it can be expressed as

\({P_a} = {P_b} = {p_c} \Rightarrow \frac{{{F_a}}}{{{A_a}}} = \frac{{{F_b}}}{{{A_b}}} = \frac{{{F_c}}}{{{A_c}}}\)

• From the above fig., we can see that the force against the area within a fluid at rest will always experience pressure perpendicular to its surface area, and the object will experience equal pressure throughout the surface.
• And there are a number of devices, such as hydraulic lifts and hydraulic brakes, which are based on Pascal’s law, these devices used fluids for transmitting pressure.

EXPLANATION:

• From the above explanation we can see that according to Pascal’s law, pressure in a fluid at rest is the same at all points if they are at the same height.
• This means option one is correct among all.

Concept:

Hydrostatic Law:

• According to Hydrostatic Law, the rate of increase of pressure in a vertical direction is equal to the weight density of the fluid at that point when the fluid is stationary.
• In hydrostatic equilibrium conditions, the force exerted by the fluid is balanced by its weight.
• Maintaining the hydrostatic balance is the key concept of buoyancy.

Consider an element shown in the above figure, let the thickness of the element be dh. For equilibrium condition;

P + \(\gamma\) × Δh = P +ΔP

\(\gamma\times \Delta h =\Delta P\)

\(\gamma={\Delta P\over \Delta h}\)

The rate of increase of pressure in a vertical direction is equal to the weight density of the fluid at that point when the fluid is stationary.

Viscosity:

• Viscosity may be defined as the property of a fluid that determines its resistance to shearing stresses. It is a measure of the internal fluid friction which causes resistance to flow. 
• It is primarily due to cohesion and molecular momentum exchange between fluid layers, and as flow occurs, these effects appear as shearing stresses between the moving layers of fluid.
• An ideal fluid has no viscosity. There is no fluid that can be classified as a perfectly ideal fluid.
• The viscosity of liquids decreases with temperature increases whereas the viscosity of gases increases with an increase in temperature.
• The S.I. unit of viscosity is Newton-second per square meter (N.s/m²).
• The C.G.S. unit of viscosity is dyne-second per square centimeter (\(dyne-sec\over cm^2\)) is also called poise.
• The viscosity of water at 20^∘C is one centipoise.

Thus both statements are correct. Hence option (2) is correct.

Concept:

Pabsolute = Patmospheric + Pgauge

The pressure at any point in a static fluid is obtained by Hydro-static law which is given by-

\(\frac{dP}{dz}=-ρ{g}\)

∴ P = -ρgz

P increases when we go down (z negative) and decreases when we go up (z positive).

where P = pressure above atmospheric pressure and h = height of the point from the free surface.

Calculation: 

Given:

h = 735 mm of Mercury, ρ_mer = 13600 Kg/m3

∴ P = ρ_mer × g × h

⇒ P = 13600× 9.81× 0.735 = 98060.76  N/m2