Short Notes: Fluid Statics | Short Notes for Mechanical Engineering PDF Download

 Page 1


Fluid Statics 
Fluid Mechanics frequently asked in GATE and other PSU exams carrying medium 
marks weightage. Fluid statics comprises of topics Pascals Law, pressure at a 
point and general equation for variation of pressure
Fluid Statics fo r GATE 2018, ESE, & Other Exams
• Fluid Statics deals with fluids at rest while Fluid Dynamics studies fluids in 
motion.
• Any force developed is only due to normal stresses i.e, pressure. Such a 
condition is termed the hydrostatic condition.
• Fluid Statics is also known as Hydrostatics.
• A static fluid can have no shearing force acting on it, and that any force 
between the fluid and the boundary must be acting at right angles to the 
boundary.
• For an element of fluid at rest, the element will be in equilibrium. The sum of 
the components of forces in any direction will be zero. The sum of the 
moments of forces on the element about any point must also be zero.
• Within a fluid, the pressure is same at all the points in all the directions.
• Pressure at the wall of any vessel is perpendicular to the wall
• Pressure due to depth is P = pgh, and is the same at any horizontal level of 
connected fluid.
Fluid Pressure at a Point
• If a fluid is Stationary, then force acting on any surface or area is 
perpendicular to that surface.
• If the force exerted on each unit area of a boundary is the same, the pressure 
is said to be uniform
Page 2


Fluid Statics 
Fluid Mechanics frequently asked in GATE and other PSU exams carrying medium 
marks weightage. Fluid statics comprises of topics Pascals Law, pressure at a 
point and general equation for variation of pressure
Fluid Statics fo r GATE 2018, ESE, & Other Exams
• Fluid Statics deals with fluids at rest while Fluid Dynamics studies fluids in 
motion.
• Any force developed is only due to normal stresses i.e, pressure. Such a 
condition is termed the hydrostatic condition.
• Fluid Statics is also known as Hydrostatics.
• A static fluid can have no shearing force acting on it, and that any force 
between the fluid and the boundary must be acting at right angles to the 
boundary.
• For an element of fluid at rest, the element will be in equilibrium. The sum of 
the components of forces in any direction will be zero. The sum of the 
moments of forces on the element about any point must also be zero.
• Within a fluid, the pressure is same at all the points in all the directions.
• Pressure at the wall of any vessel is perpendicular to the wall
• Pressure due to depth is P = pgh, and is the same at any horizontal level of 
connected fluid.
Fluid Pressure at a Point
• If a fluid is Stationary, then force acting on any surface or area is 
perpendicular to that surface.
• If the force exerted on each unit area of a boundary is the same, the pressure 
is said to be uniform
u 1 S t
Pascal's Law for Pressure At A Point
• It states that pressure or intensity of pressure at a point in a static fluid (fluid 
is in rest) is equal in all directions. If fluid is not in motion then according to 
Pascal’s law,
Px = Py = Pz
where, pX i py and pz are the pressure at point x,y,z respectively. 
General Equation For Variation Of Pressure In A Static Fluid
A cylindrical element of fluid at an arbitrary orientation:
dp a
— = — p g cos & 
ds
Vertical Variation Of Pressure In A Fluid Under Gravity
Page 3


Fluid Statics 
Fluid Mechanics frequently asked in GATE and other PSU exams carrying medium 
marks weightage. Fluid statics comprises of topics Pascals Law, pressure at a 
point and general equation for variation of pressure
Fluid Statics fo r GATE 2018, ESE, & Other Exams
• Fluid Statics deals with fluids at rest while Fluid Dynamics studies fluids in 
motion.
• Any force developed is only due to normal stresses i.e, pressure. Such a 
condition is termed the hydrostatic condition.
• Fluid Statics is also known as Hydrostatics.
• A static fluid can have no shearing force acting on it, and that any force 
between the fluid and the boundary must be acting at right angles to the 
boundary.
• For an element of fluid at rest, the element will be in equilibrium. The sum of 
the components of forces in any direction will be zero. The sum of the 
moments of forces on the element about any point must also be zero.
• Within a fluid, the pressure is same at all the points in all the directions.
• Pressure at the wall of any vessel is perpendicular to the wall
• Pressure due to depth is P = pgh, and is the same at any horizontal level of 
connected fluid.
Fluid Pressure at a Point
• If a fluid is Stationary, then force acting on any surface or area is 
perpendicular to that surface.
• If the force exerted on each unit area of a boundary is the same, the pressure 
is said to be uniform
u 1 S t
Pascal's Law for Pressure At A Point
• It states that pressure or intensity of pressure at a point in a static fluid (fluid 
is in rest) is equal in all directions. If fluid is not in motion then according to 
Pascal’s law,
Px = Py = Pz
where, pX i py and pz are the pressure at point x,y,z respectively. 
General Equation For Variation Of Pressure In A Static Fluid
A cylindrical element of fluid at an arbitrary orientation:
dp a
— = — p g cos & 
ds
Vertical Variation Of Pressure In A Fluid Under Gravity
P2, A
A rea A
Taking upward as positive, we have
Vertical cylindrical element of fluid cross sectional area = A
mass density = p
The forces involved are:
• Force due to pi on A (upward) = p ^
• Force due to P 2 on A (downward) = P 2A
• Force due to weight of element (downward) = mg
Thus in a fluid under gravity, pressure decreases linearly with increase in height
P 2 - Pi = pg(z2 - z i)
This is the hydrostatic pressure change.
Equality Of Pressure At The Same Level In A Static Fluid
Horizontal cylindrical element cross sectional area = A 
mass density =p 
left end pressure = pi 
right end pressure = pr
For equilibrium, the sum of the forces in the x direction is zero= pi A = pr A
P i = Pr
so, Pressure in the horizontal direction is constant
= mass density x volume x g 
= pgA(z2 -z 1 )
V
w e ig h t, m g
Page 4


Fluid Statics 
Fluid Mechanics frequently asked in GATE and other PSU exams carrying medium 
marks weightage. Fluid statics comprises of topics Pascals Law, pressure at a 
point and general equation for variation of pressure
Fluid Statics fo r GATE 2018, ESE, & Other Exams
• Fluid Statics deals with fluids at rest while Fluid Dynamics studies fluids in 
motion.
• Any force developed is only due to normal stresses i.e, pressure. Such a 
condition is termed the hydrostatic condition.
• Fluid Statics is also known as Hydrostatics.
• A static fluid can have no shearing force acting on it, and that any force 
between the fluid and the boundary must be acting at right angles to the 
boundary.
• For an element of fluid at rest, the element will be in equilibrium. The sum of 
the components of forces in any direction will be zero. The sum of the 
moments of forces on the element about any point must also be zero.
• Within a fluid, the pressure is same at all the points in all the directions.
• Pressure at the wall of any vessel is perpendicular to the wall
• Pressure due to depth is P = pgh, and is the same at any horizontal level of 
connected fluid.
Fluid Pressure at a Point
• If a fluid is Stationary, then force acting on any surface or area is 
perpendicular to that surface.
• If the force exerted on each unit area of a boundary is the same, the pressure 
is said to be uniform
u 1 S t
Pascal's Law for Pressure At A Point
• It states that pressure or intensity of pressure at a point in a static fluid (fluid 
is in rest) is equal in all directions. If fluid is not in motion then according to 
Pascal’s law,
Px = Py = Pz
where, pX i py and pz are the pressure at point x,y,z respectively. 
General Equation For Variation Of Pressure In A Static Fluid
A cylindrical element of fluid at an arbitrary orientation:
dp a
— = — p g cos & 
ds
Vertical Variation Of Pressure In A Fluid Under Gravity
P2, A
A rea A
Taking upward as positive, we have
Vertical cylindrical element of fluid cross sectional area = A
mass density = p
The forces involved are:
• Force due to pi on A (upward) = p ^
• Force due to P 2 on A (downward) = P 2A
• Force due to weight of element (downward) = mg
Thus in a fluid under gravity, pressure decreases linearly with increase in height
P 2 - Pi = pg(z2 - z i)
This is the hydrostatic pressure change.
Equality Of Pressure At The Same Level In A Static Fluid
Horizontal cylindrical element cross sectional area = A 
mass density =p 
left end pressure = pi 
right end pressure = pr
For equilibrium, the sum of the forces in the x direction is zero= pi A = pr A
P i = Pr
so, Pressure in the horizontal direction is constant
= mass density x volume x g 
= pgA(z2 -z 1 )
V
w e ig h t, m g
As we know, pi = pr
For a ve rtic a l pre ssu re change w e have
P i = P p + P S 2
and
Pr = Pq+Pgz 
so
Pp+Pgz = Pq +P& 
Pp=Pq
The pressure at the two equal levels is the same.