• The viscosity of a fluid is to be measured by a viscometer
constructed of two 40-cm-long concentric cylinders. The outer
diameter of the inner cylinder is 12 cm, and the gap between
the two cylinders is 0.15 cm. The inner cylinder is rotated at
300 rpm, and the torque is measured to be 1.8 N-m.
Determine the viscosity of the fluid.
Non-Newtonian fluids:
• For non-Newtonian fluids, the relationship
between shear stress and rate of deformation
is not linear, as shown in Fig.
• The slope of the curve on the τ versus du/dy
chart is referred to as the apparent viscosity of
the fluid.
• Fluids for which the apparent viscosity
increases with the rate of deformation (such
as solutions with suspended starch or sand)
are referred to as dilatant or shear thickening
fluids,
• Pseudoplastic or shear thinning fluids: The fluid
which becomes less viscous as it is sheared harder,
such as some paints, polymer solutions, and fluids
with suspended particles)
Eg: ketchup, whipped cream, blood, paint, and nail
polish.
• Bingham plastics: Some materials can resist a finite
shear stress and thus behave as a solid, but deform
continuously when the shear stress exceeds the yield
stress and thus behave as a fluid.
Eg: toothpaste
Examples of Bingham Plastic
Mayonnaise
Drilling Mud
Tooth Paste
Numerical
• The following results were obtained for 3 substances during
an experiment. Classify them as solid, Newtonian and NonNewtonian fluid. Also name the non-Newtonian fluid type.
A
du/dy
τ
0
2
1
3
2
4
3
5
B
du/dy
τ
0
2
0
3
0
4
0
5
C
du/dy
τ
0
0
1
1
2
2
3
3
• Pressure
Pressure is the normal compressive force exerted by
a fluid per unit area.
Pressure comes into consideration only when we
deal with a gas or a liquid.
The counterpart of pressure in solids is normal
stress.
Pressure at any point in a fluid is the same in all
directions.
It has magnitude but not a specific direction, and
thus it is a scalar quantity.
• Absolute Pressure and Gauge Pressure:-
Two basic pressure gages
• Measurement of Pressure
INTRODUCTION TO FLUID STATICS
Fluid statics deals with problems associated with fluids at rest.
In fluid statics, there is no relative motion between adjacent fluid layers, and
thus there are no shear (tangential) stresses in the fluid trying to deform it.
The only stress we deal with in fluid statics is the normal stress, which is the
pressure, and the variation of pressure is due only to the weight of the fluid.
Fluid statics is used to determine the forces acting on floating or submerged
bodies and the forces developed by devices like hydraulic presses
and car jacks.
The design of many engineering systems such as water dams and liquid
storage tanks requires the determination of the forces acting on the surfaces
using fluid statics.
To determine the variation of pressure
in a fluid at rest :
Variation of pressure in a fluid at rest :
Consider a rectangular fluid element of
height Δ z, length Δ x, and unit depth (into
the page) in equilibrium, as shown in Fig.
Assuming the density of the fluid ρ to
be constant, a force balance in the vertical
z-direction gives:
where W = mg = ρgΔx Δz is the weight of the fluid element.
Dividing by Δ x and rearranging gives:
P2 = P1 + ρgΔz
Pascal’s law
The pressure applied to a confined fluid increases the
pressure throughout by the same amount. This is called
Pascal’s law, after Blaise Pascal (1623–1662).
Pascal also knew that the force applied by a
fluid is proportional to the surface area.
Hydraulic brakes and lifts etc are based on Pascal’s law.
Hydraulic lifts:
The area ratio A2/A1 is called the ideal mechanical advantage of
the hydraulic lift.
THE MANOMETER
A device based on this principle is called a manometer,
and it is commonly used to measure small and moderate
pressure differences. A manometer mainly consists of a
glass or plastic U-tube containing one or more fluids such
as mercury, water, alcohol, or oil. To keep the size of the
manometer to a manageable level, heavy fluids such as
mercury are used if large pressure differences are
anticipated.
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