Capillary rise on Black Hole

CAPILLARY RISE ON SURFACE OF BLACK HOLE

INTRODUCTION

Capillarity or capillary action is the ability of a liquid to flow in narrow spaces without the assistance of external forces. When a capillary tube is inserted into a beaker containing liquid, the level of liquid in the capillary tend to rise or fall depending on the angle of contact between liquid and the tube wall. We intend to study only the rise of liquid in a capillary tube. Since the liquid rises against gravity, the extent to which it can rise also directly depends on the local acceleration due to gravity. We thus intend to determine the extent of capillary rise by a liquid on the surface of Black hole.

ASSUMPTIONS

1. The local acceleration due to gravity is constant and not varying continuously

2. The angle of contact is always acute

3. The liquid is free from impurities

4. Temperature of the liquid is constant

5. The capillary tube is indestructible

6. Space time deformation has no effect on capillarity phenomenon

CALCULATION

Consider a liquid [pure water] of density ‘ρ’ in a glass beaker with an inverted glass capillary tube inserted in a beaker as shown in figure.1. Let ‘r’ be the radius of the capillary tube, ‘θ’ be the angle of contact between pure water and the wall of capillary tube and ‘T’ be the surface tension of water.

Fig .1 Capillarity

The equation for capillary rise ‘h’ in the tube is given by,

h – Capillary rise in the tube (m)

T – Surface tension of water [T = 7.28*10^-2 N/m]

θ – Angle of contact between pure water and glass tube [θ = 0°]

ρ – Density of water [ρ = 1000 Kg/m³]

r – Radius of capillary tube [r = 1.5 *10^-3 m]

g – Acceleration due to gravity on event horizon of Black hole [g = ꝏ m/s²]

Substituting the constants in equation (1),

The cohesive and adhesive forces of liquid cannot overcome the extreme gravitational pull of a black hole, hence the capillary rise is zero.

CONCLUSION

We thus determined the capillary rise of water on the surface of Black hole. It is interesting to note that the capillary rise does not depend on the length of the capillary tube.

Capillary rise on Neutron star

CAPILLARY RISE ON SURFACE OF NEUTRON STAR

INTRODUCTION

Capillarity or capillary action is the ability of a liquid to flow in narrow spaces without the assistance of external forces. When a capillary tube is inserted into a beaker containing liquid, the level of liquid in the capillary tend to rise or fall depending on the angle of contact between liquid and the tube wall. We intend to study only the rise of liquid in a capillary tube. Since the liquid rises against gravity, the extent to which it can rise also directly depends on the local acceleration due to gravity. We thus intend to determine the extent of capillary rise by a liquid on the surface of Neutron Star.

ASSUMPTIONS

1. The local acceleration due to gravity is constant and not varying continuously

2. The angle of contact is always acute

3. The liquid is free from impurities

4. Temperature of the liquid is constant

5. The capillary tube is indestructible

6. Space time curvature does not impede capillary rise of liquid

CALCULATION

Consider a liquid [pure water] of density ‘ρ’ in a glass beaker with an inverted glass capillary tube inserted in a beaker as shown in figure.1. Let ‘r’ be the radius of the capillary tube, ‘θ’ be the angle of contact between pure water and the wall of capillary tube and ‘T’ be the surface tension of water.

Fig .1 Capillarity

The equation for capillary rise ‘h’ in the tube is given by,

h – Capillary rise in the tube (m)

T – Surface tension of water [T = 7.28*10^-2 N/m]

θ – Angle of contact between pure water and glass tube [θ = 0°]

ρ – Density of water [ρ = 1000 Kg/m³]

r – Radius of capillary tube [r = 1.5 *10^-3 m]

g – Acceleration due to gravity on Neutron Star [g = 7*10¹² m/s²]

Substituting the constants in equation (1),

The capillary rise is extremely small owing to the fact that gravitational attraction is very strong on a Neutron star. This rise may not be quantifiably meaningful.

CONCLUSION

We thus determined the capillary rise of water on the surface of Neutron Star. It is interesting to note that the capillary rise does not depend on the length of the capillary tube.

High frequency sine sweep test: 4KHz to 16KHz

Capillary rise on surface of Sun

CAPILLARY RISE ON SURFACE OF SUN

INTRODUCTION

Capillarity or capillary action is the ability of a liquid to flow in narrow spaces without the assistance of external forces. When a capillary tube is inserted into a beaker containing liquid, the level of liquid in the capillary tend to rise or fall depending on the angle of contact between liquid and the tube wall. We intend to study only the rise of liquid in a capillary tube. Since the liquid rises against gravity, the extent to which it can rise also directly depends on the local acceleration due to gravity. We thus intend to determine the extent of capillary rise by a liquid on the surface of Sun.

ASSUMPTIONS

1. The local acceleration due to gravity is constant and not varying continuously

2. The angle of contact is always acute

3. The liquid is free from impurities

4. Temperature of the liquid is constant

5. The capillary tube is indestructible

CALCULATION

Consider a liquid [pure water] of density ‘ρ’ in a glass beaker with an inverted glass capillary tube inserted in a beaker as shown in figure.1. Let ‘r’ be the radius of the capillary tube, ‘θ’ be the angle of contact between pure water and the wall of capillary tube and ‘T’ be the surface tension of water.

Fig .1 Capillarity

The equation for capillary rise ‘h’ in the tube is given by,

h – Capillary rise in the tube (m)

T – Surface tension of water [T = 7.28*10^-2 N/m]

θ – Angle of contact between pure water and glass tube [θ = 0°]

ρ – Density of water [ρ = 1000 Kg/m³]

r – Radius of capillary tube [r = 1.5 *10^-3 m]

g – Acceleration due to gravity on Sun [g = 273.7 m/s²]

Substituting the constants in equation (1),

This value of capillary rise is small compared to all the other planets. In fact it is 30 times smaller than the rise on Earth.

CONCLUSION

We thus determined the capillary rise of water on the surface of Sun. It is interesting to note that the capillary rise does not depend on the length of the capillary tube.

Capillary rise on surface of Jupiter

CAPILLARY RISE ON SURFACE OF JUPITER

INTRODUCTION

Capillarity or capillary action is the ability of a liquid to flow in narrow spaces without the assistance of external forces. When a capillary tube is inserted into a beaker containing liquid, the level of liquid in the capillary tend to rise or fall depending on the angle of contact between liquid and the tube wall. We intend to study only the rise of liquid in a capillary tube. Since the liquid rises against gravity, the extent to which it can rise also directly depends on the local acceleration due to gravity. We thus intend to determine the extent of capillary rise by a liquid on the surface of Jupiter.

ASSUMPTIONS

1. The local acceleration due to gravity is constant and not varying continuously

2. The angle of contact is always acute

3. The liquid is free from impurities

4. Temperature of the liquid is constant

5. The capillary tube is indestructible

CALCULATION

Consider a liquid [pure water] of density ‘ρ’ in a glass beaker with an inverted glass capillary tube inserted in a beaker as shown in figure.1. Let ‘r’ be the radius of the capillary tube, ‘θ’ be the angle of contact between pure water and the wall of capillary tube and ‘T’ be the surface tension of water.

Fig .1 Capillarity

The equation for capillary rise ‘h’ in the tube is given by,

h – Capillary rise in the tube (m)

T – Surface tension of water [T = 7.28*10^-2 N/m]

θ – Angle of contact between pure water and glass tube [θ = 0°]

ρ – Density of water [ρ = 1000 Kg/m³]

r – Radius of capillary tube [r = 1.5 *10^-3 m]

g – Acceleration due to gravity on Jupiter [g = 24.5 m/s²]

Substituting the constants in equation (1),

Thus water will rise by approximately 4mm on Jupiter. It is also one third the amount of the rise on Earth.

CONCLUSION

We thus determined the capillary rise of water on the surface of Jupiter. It is interesting to note that the capillary rise does not depend on the length of the capillary tube.

Frequency sweep test 250Hz to 4000Hz

Capillary rise inside International Space Station

CAPILLARY RISE INSIDE INTERNATIONAL SPACE STATION

INTRODUCTION

Capillarity or capillary action is the ability of a liquid to flow in narrow spaces without the assistance of external forces. When a capillary tube is inserted into a beaker containing liquid, the level of liquid in the capillary tend to rise or fall depending on the angle of contact between liquid and the tube wall. We intend to study only the rise of liquid in a capillary tube. Since the liquid rises against gravity, the extent to which it can rise also directly depends on the local acceleration due to gravity. We thus intend to determine the extent of capillary rise by a liquid inside the International Space Station (ISS).

ASSUMPTIONS

1. The angle of contact is always acute

2. The liquid is free from impurities

3. Temperature of the liquid is constant

4. The capillary tube is indestructible

CALCULATION

Consider a liquid [pure water] of density ‘ρ’ in a glass beaker with an inverted glass capillary tube inserted in a beaker as shown in figure.1. Let ‘r’ be the radius of the capillary tube, ‘θ’ be the angle of contact between pure water and the wall of capillary tube and ‘T’ be the surface tension of water. The ISS is orbiting the Earth hence always in a state of free fall. This means that objects inside will not experience any acceleration and hence safe to assume that gravity is zero.

Fig .1 Capillarity

The equation for capillary rise ‘h’ in the tube is given by,

h – Capillary rise in the tube (m)

T – Surface tension of water [T = 7.28*10^-2 N/m]

θ – Angle of contact between pure water and glass tube [θ = 0°]

ρ – Density of water [ρ = 1000 Kg/m³]

r – Radius of capillary tube [r = 1.5 *10^-3 m]

g – Acceleration due to gravity on ISS [g = 0 m/s²]

Substituting the constants in equation (1),

Since gravitational acceleration is not present inside the space station due to free fall, the capillary rise would be infinite. This implies that as soon as water comes in contact with the capillary tube, it will be ejected out of the tube like a jet.

CONCLUSION

We thus determined the capillary rise of water inside the ISS. It is interesting to note that the capillary rise does not depend on the length of the capillary tube.

Alarm Clock Sound

Capillary Rise on Surface of Moon

CAPILLARY RISE ON SURFACE OF MOON

INTRODUCTION

Capillarity or capillary action is the ability of a liquid to flow in narrow spaces without the assistance of external forces. When a capillary tube is inserted into a beaker containing liquid, the level of liquid in the capillary tend to rise or fall depending on the angle of contact between liquid and the tube wall. We intend to study only the rise of liquid in a capillary tube. Since the liquid rises against gravity, the extent to which it can rise also directly depends on the local acceleration due to gravity. We thus intend to determine the extent of capillary rise by a liquid on the surface of Moon.

ASSUMPTIONS

1. The local acceleration due to gravity is constant and not varying continuously

2. The angle of contact is always acute

3. The liquid is free from impurities

4. Temperature of the liquid is constant

CALCULATION

Consider a liquid [pure water] of density ‘ρ’ in a glass beaker with an inverted glass capillary tube inserted in a beaker as shown in figure.1. Let ‘r’ be the radius of the capillary tube, ‘θ’ be the angle of contact between pure water and the wall of capillary tube and ‘T’ be the surface tension of water.

Fig .1 Capillary rise

The equation for capillary rise ‘h’ in the tube is given by

h – Capillary rise in the tube (m)

T – Surface tension of water [T = 7.28*10^-2 N/m]

θ – Angle of contact between pure water and glass tube [θ = 0°]

ρ – Density of water [ρ = 1000 Kg/m³]

r – Radius of capillary tube [r = 1.5 *10^-3 m]

g – Acceleration due to gravity on Moon [g = 1.62 m/s²]

Substituting the constants in equation (1),

The capillary rise is approximately 6cm. It is also approximately 6 times greater than the rise on Earth.

CONCLUSION

We thus determined the capillary rise of water on the surface of Moon. It is interesting to note that the capillary rise does not depend on the length of the capillary tube.

Capillary rise on surface of Earth

CAPILLARY RISE ON SURFACE OF EARTH

INTRODUCTION

Capillarity or capillary action is the ability of a liquid to flow in narrow spaces without the assistance of external forces. When a capillary tube is inserted into a beaker containing liquid, the level of liquid in the capillary tend to rise or fall depending on the angle of contact between liquid and the tube wall. We intend to study only the rise of liquid in a capillary tube. Since the liquid rises against gravity, the extent to which it can rise also directly depends on the local acceleration due to gravity. We thus intend to determine the extent of capillary rise by a liquid on the surface of Earth.

ASSUMPTIONS

1. The local acceleration due to gravity is constant and not varying continuously

2. The angle of contact is always acute

3. The liquid is free from impurities

4. Temperature of the liquid is constant

CALCULATION

Consider a liquid [pure water] of density ‘ρ’ in a glass beaker with an inverted glass capillary tube inserted in a beaker as shown in figure.1. Let ‘r’ be the radius of the capillary tube, ‘θ’ be the angle of contact between pure water and the wall of capillary tube and ‘T’ be the surface tension of water.

Fig .1 Capillary rise

The equation for capillary rise ‘h’ in the tube is given by,

h – Capillary rise in the tube (m)

T – Surface tension of water [T = 7.28*10^-2 N/m]

θ – Angle of contact between pure water and glass tube [θ = 0°]

ρ – Density of water [ρ = 1000 Kg/m³]

r – Radius of capillary tube [r = 1.5 *10^-3 m]

g – Acceleration due to gravity on Earth [g = 9.8 m/s²]

Substituting the constants in equation (1),

Hence the capillary rise for the given configuration is 9.9mm

CONCLUSION

We thus determined the capillary rise of water on the surface of Earth. It is interesting to note that the capillary rise does not depend on the length of the capillary tube.

Center of gravity of two distinct shapes Pt2

CENTER OF GRAVITY OF TWO DISTINCT SHAPES PT2

INTRODUCTION

The center of gravity COG of an object is the point of action of the gravitational force. It is also known as the balancing point since all objects [simple or complex] have their COG within the object’s sphere of influence and this ensures stability. There are two values to be noted which is the geometrical center of gravity and the actual center of gravity. The geometrical COG is the exact center of the object. It can be calculated by various available methods like summation, moment of inertia, etc. The geometrical COG is valid as long as there is uniform distribution of mass and or uniform gravitational field. In case of uneven mass distribution or use of composite or heterogeneous materials, the actual COG will no longer coincide with the geometrical COG. This is because mass is distributed unevenly and the COG will shift where there is more mass. In this article we intend to determine the COG of an assembly of an isosceles triangle and a semi-circle.

ASSUMPTIONS

1. Mass of the object is evenly distributed

2. The gravitational field is uniform

3. The semi-circle accurately fits inside the triangle

CALCULATION

Consider a semi-circle inscribed in an isosceles triangle such that the diameter of the semi-circle coincides with the base of the isosceles triangle. This orientation is represented in figure.1. The triangle has height ‘h’, side length ‘b’ and base ‘a’. The diameter of the semi-circle is connected to the base of the triangle, hence the diameter is ‘a’ and thereby the radius is ‘a/2’ or ‘r’ where r = a/2

Fig .1 Triangle and semi-circle

We will determine the center of gravity using the area moment of inertia method. We need to follow four steps:

1    1. Determine the distance between the x coordinate of C.O.G. of (triangle and semi-circle) and reference Y axis.

2    2. Determine the distance between the y coordinate of C.O.G. of (triangle and semi-circle) and reference X axis.

3      3. Determine the area of two objects in question.

4      4. Use the Summation equation to determine the C.O.G. coordinates.

It is evident that the assembly represented in figure.1 is symmetric about y axis, hence x coordinates of both triangle and semi-circle will be their midpoint. The y coordinates are same for isosceles triangle and semi-circle.

The coordinates and areas of triangle and semi-circle are as follows

Isosceles triangle

X₁ = r, Y₁ = h/3

A₁ = (1/2)*2r*h = h*r

Semi-circle

X₂ = r, Y₂ = 4r/3π

A­₂ = (1/2)*π*r² = πr²/2

Center of gravity

The center of gravity coordinates x and y of the assembly can be computed by using the formula,

Negative sign in above equations indicate that the second part (semi-circle) is being subtracted from the whole assembly.

CONCLUSION

Thus the center of gravity of the given assembly is located at