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Fluid is something that can flow therefore liquids and gases come in this category. A perfect liquid cannot be compressed and shearing stress cannot be maintained.
Streamlined steady state flow by steady state or stationary flow we mean that at any place in a fluid the velocity never changes.
Streamline is a curve tangent to which at any point gives the direction of fluid velocity at that point.
Equation of continuity volume entering per second = volume leaving per second
Or A1 v1 = A2 v2
Where A and A2 are area of cross-sections and v1 and v2 are velocities at the two ends/points of a pipe.
Bernoulli’s theorem it states that the total energy is constant.
KE + PE + pressure head Energy = constant
1/2 mv2 + mgh + P∆V = constant
Or 1/2 pv2 + pgh + P = constant
In a horizontal pipe 1/2 pv2 + P = constant
Torricelli’s theorem according to this theorem velocity of efflux v efflux = √2g (H- h)
Velocity of efflux from a closed vessel if P is pressure inside
P = Pa + 1/2 pv2
V = √2(P – Pa)/P
Where Pa = atmospheric pressure.
Dynamic lift or Magnus effect when a ball is spinning in a fluid as illustrated in the resultant velocity below the ball decreases and the ball experiences an upward thrust, such a phenomenon is called dynamic lift or Magnus effect.
Venturimeter P1 – P2 = Hgp
P1/pg + v12/2g = P2/g + V22/2g
P1 – p2/pg = v22 – v12/2g
Hpg/pg = v2/2g [1/a2 – 1/A2] or v/t = aA √2gH/A2 – a2
Surface tension the property of the liquid with which its surface behaves as a stretched membrane and can support small objects placed on its surface.
Surface tension = surface energy
Surface energy = work done due to surface tension/area
Dimensional formula (MT-2) (force/length)
Consider two molecules of a liquid, one inside like A and one on the surface like B.A is completely balanced due to forces exerted by other molecules of the liquid. B has unbalanced forces. This figure demonstrates why the surface of the liquid behaves as a stretched membrane. The molecular force between the molecules of the liquid is cohesive force. Due to surface tension a liquid would try to acquire minimum surface area with maximum volume,
Excess pressure in a drop/ bubble ∆P = 2T/r
Where T is surface tension and r is radius.
If a bubble has two free surfaces, like soap bubble,
Then the excess pressure is ∆P = 4T/r
Angle of contact is the angle between the tangent to the liquid vapor interface and the tangent to liquid solid interface. In other words, it is the angle between the tangent to the meniscus at the point of contact and wall of the container.
Liquids like water, alcohol ether carbon tetrachloride x Ilene, glycerin and acetic acid have angle of contact zero or nearly zero with glass. Meniscus may be concaving upward or convex upward.
Fluid is something that can flow therefore liquids and gases come in this category. A perfect liquid cannot be compressed and shearing stress cannot be maintained.
Streamlined steady state flow by steady state or stationary flow we mean that at any place in a fluid the velocity never changes.
Streamline is a curve tangent to which at any point gives the direction of fluid velocity at that point.
Equation of continuity volume entering per second = volume leaving per second
Or A1 v1 = A2 v2
Where A and A2 are area of cross-sections and v1 and v2 are velocities at the two ends/points of a pipe.
Bernoulli’s theorem it states that the total energy is constant.
KE + PE + pressure head Energy = constant
1/2 mv2 + mgh + P∆V = constant
Or 1/2 pv2 + pgh + P = constant
In a horizontal pipe 1/2 pv2 + P = constant
Torricelli’s theorem according to this theorem velocity of efflux v efflux = √2g (H- h)
Velocity of efflux from a closed vessel if P is pressure inside
P = Pa + 1/2 pv2
V = √2(P – Pa)/P
Where Pa = atmospheric pressure.
Dynamic lift or Magnus effect when a ball is spinning in a fluid as illustrated in the resultant velocity below the ball decreases and the ball experiences an upward thrust, such a phenomenon is called dynamic lift or Magnus effect.
Venturimeter P1 – P2 = Hgp
P1/pg + v12/2g = P2/g + V22/2g
P1 – p2/pg = v22 – v12/2g
Hpg/pg = v2/2g [1/a2 – 1/A2] or v/t = aA √2gH/A2 – a2
Surface tension the property of the liquid with which its surface behaves as a stretched membrane and can support small objects placed on its surface.
Surface tension = surface energy
Surface energy = work done due to surface tension/area
Dimensional formula (MT-2) (force/length)
Consider two molecules of a liquid, one inside like A and one on the surface like B.A is completely balanced due to forces exerted by other molecules of the liquid. B has unbalanced forces. This figure demonstrates why the surface of the liquid behaves as a stretched membrane. The molecular force between the molecules of the liquid is cohesive force. Due to surface tension a liquid would try to acquire minimum surface area with maximum volume,
Excess pressure in a drop/ bubble ∆P = 2T/r
Where T is surface tension and r is radius.
If a bubble has two free surfaces, like soap bubble,
Then the excess pressure is ∆P = 4T/r
Angle of contact is the angle between the tangent to the liquid vapor interface and the tangent to liquid solid interface. In other words, it is the angle between the tangent to the meniscus at the point of contact and wall of the container.
Liquids like water, alcohol ether carbon tetrachloride x Ilene, glycerin and acetic acid have angle of contact zero or nearly zero with glass. Meniscus may be concaving upward or convex upward.
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