Hydraulics and Hydrometric summary
1. Introduction
Open water = water in ditcher, rivers and streams.
1.2 Water and physics
Hydrostatics and hydrodynamics have water, fluids in general as subjects.
Newton’s second law
F=mxa
a = dv/dt
Velocity of a body can change in time (dv/dt) under a Force. This Force = mass x acceleration.
Another field of physics has no fixed shape. Properties of fluids that are investigated are velocity,
pressure, density and temperature especially water.
Physics can be divided into statics and dynamics, water is in hydrostatics and hydrodynamics.
1.3 Mass and weight
P = mass / volume p (water) = 1000 kg/m^3
Weight (w) = gravitational force (Fgrav) of earth on an object W = Fgrav = m g.
1.4 Water as a fluid
Shear stress = lower layers of the water however, resist by a dragging force. Resulting in gradually
diminishing velocities to the bottom.
Viscosity = resistance of a fluid that is dragged along by neighboring layers of the fluid. The more viscous
a fluid is, the thicker it is and slower it deforms under stress. This is expressed by u.
Ideal fluid = no viscosity.
Capillary force = water flowing through narrow tubes.
2 Hydrostatic pressure
Hydrostatic situation means that the water is not flowing (standing water). Flow velocity is 0.
2.1 What’s pressure
Pressure = the force applied perpendicular to the surface of an object per unit area over which that force
is distributed. (N/m^2).
Earth has atmospheric pressure, which has a value P = 101 x 10^3 N/m^3. It’s assumed that this value is
constant.
Gauge pressure = the pressure relative to the atmospheric pressure.
P (absolute) = Pgauge + P atmosphere.
, 2.2 Pressure in water
The water surface of standing water is always horizontal. The pressure can be computed by
P = p g z (z is water depth below the free surface).
The pressure increases linearly with the depth.
2.3 Hydrostatic paradox
Hydrostatic paradox = difference between pressure exerted by rigid bodies and in fluids.
In the figure you can see three block with surface A and weight W:
W 2W
Pl= Pr= Pr=2 Pl
A A
The right figure you can calculate the pressure with the
formula P = p g z in which Pr = Pl. In a fluid the depth
below the free surface is important and not the
weight/mass above it.
Solid doesn’t change its shape under pressure while
fluid is deformable. The shape of the vessel and the
bottom area don’t matter.
There’s also no difference in pressure horizontal.
In hydrostatics the fluids are at rest. The difference in levels between left and right part would generate
difference in left-right-pressures, which isn’t possible in a standing fluid.
Pascal’s law = only magnitude of pressure is
given by the equation P = pgz no direction
needed. Pressure is a scaler and not a
magnitude.
2.4 calculating pressure
Notation Z is used for height and uses unit M.
The gauge pressure is expressed in N/m^-2.
Negative pressure can occur, it means less than
atmospheric pressure.
Within same fluid:
Pressure do not differ horizontal
Pressure difference vertical are given
by p g z.
2.5 measuring pressure flowing water
Hydrostatic pressure in cases of flowing water
L-shaped piezometer is attached
Contains standing water. The law: Pa = Pb = p g h
Pa is used to measure water pressure in point A of flowing water.
1. Introduction
Open water = water in ditcher, rivers and streams.
1.2 Water and physics
Hydrostatics and hydrodynamics have water, fluids in general as subjects.
Newton’s second law
F=mxa
a = dv/dt
Velocity of a body can change in time (dv/dt) under a Force. This Force = mass x acceleration.
Another field of physics has no fixed shape. Properties of fluids that are investigated are velocity,
pressure, density and temperature especially water.
Physics can be divided into statics and dynamics, water is in hydrostatics and hydrodynamics.
1.3 Mass and weight
P = mass / volume p (water) = 1000 kg/m^3
Weight (w) = gravitational force (Fgrav) of earth on an object W = Fgrav = m g.
1.4 Water as a fluid
Shear stress = lower layers of the water however, resist by a dragging force. Resulting in gradually
diminishing velocities to the bottom.
Viscosity = resistance of a fluid that is dragged along by neighboring layers of the fluid. The more viscous
a fluid is, the thicker it is and slower it deforms under stress. This is expressed by u.
Ideal fluid = no viscosity.
Capillary force = water flowing through narrow tubes.
2 Hydrostatic pressure
Hydrostatic situation means that the water is not flowing (standing water). Flow velocity is 0.
2.1 What’s pressure
Pressure = the force applied perpendicular to the surface of an object per unit area over which that force
is distributed. (N/m^2).
Earth has atmospheric pressure, which has a value P = 101 x 10^3 N/m^3. It’s assumed that this value is
constant.
Gauge pressure = the pressure relative to the atmospheric pressure.
P (absolute) = Pgauge + P atmosphere.
, 2.2 Pressure in water
The water surface of standing water is always horizontal. The pressure can be computed by
P = p g z (z is water depth below the free surface).
The pressure increases linearly with the depth.
2.3 Hydrostatic paradox
Hydrostatic paradox = difference between pressure exerted by rigid bodies and in fluids.
In the figure you can see three block with surface A and weight W:
W 2W
Pl= Pr= Pr=2 Pl
A A
The right figure you can calculate the pressure with the
formula P = p g z in which Pr = Pl. In a fluid the depth
below the free surface is important and not the
weight/mass above it.
Solid doesn’t change its shape under pressure while
fluid is deformable. The shape of the vessel and the
bottom area don’t matter.
There’s also no difference in pressure horizontal.
In hydrostatics the fluids are at rest. The difference in levels between left and right part would generate
difference in left-right-pressures, which isn’t possible in a standing fluid.
Pascal’s law = only magnitude of pressure is
given by the equation P = pgz no direction
needed. Pressure is a scaler and not a
magnitude.
2.4 calculating pressure
Notation Z is used for height and uses unit M.
The gauge pressure is expressed in N/m^-2.
Negative pressure can occur, it means less than
atmospheric pressure.
Within same fluid:
Pressure do not differ horizontal
Pressure difference vertical are given
by p g z.
2.5 measuring pressure flowing water
Hydrostatic pressure in cases of flowing water
L-shaped piezometer is attached
Contains standing water. The law: Pa = Pb = p g h
Pa is used to measure water pressure in point A of flowing water.
