According to Bernoulli’s equation, discharge varies as the square root of the pressure difference.

It includes both energy losses and contraction effects, correcting theoretical flow rate.

For a V-notch, discharge is proportional to h^(5/2), providing higher sensitivity for small flows.

Weirs are barriers across open channels that allow flow measurement by head variation.

Flow rate is proportional to √h because it follows Bernoulli’s principle.

Smooth flow and gradual contraction in a Venturi meter minimize energy losses.

Higher pressure difference means greater velocity and thus greater discharge.

Coefficient of velocity indicates actual to theoretical velocity ratio, usually about 0.98.

Rectangular notches are best for measuring large discharges accurately.

Discharge coefficient changes slightly with Reynolds number due to viscous effects.

Flow becomes choked at critical pressure, giving maximum discharge

It measures the dynamic pressure to calculate velocity using Bernoulli’s principle

Orifice meters cause greater head loss due to sharp-edged plates and flow separation

V-notches provide accurate measurement for small discharges because of their sensitivity.

Notches (like rectangular or V-notch) are used to measure flow rates in open channels.

The Venturi meter has a high coefficient of discharge (~0.98) due to low energy loss.

A Pitot tube measures the stagnation and static pressure difference to directly find the flow velocity.

The flow rate in an Orifice meter is calculated using the pressure drop across the orifice plate.

Velocity is maximum at the throat, so pressure is minimum due to energy conservation.

The Venturi meter measures flow using pressure difference between the throat and inlet, based on Bernoulli’s theorem

The total energy line includes both pressure and velocity heads, so it’s always above the hydraulic gradient.

For steady flow in a horizontal pipe, energy losses are uniform, keeping lines parallel.

Higher pressure difference means higher velocity and hence greater flow rate.

In laminar regime, head loss ∝ velocity, while in turbulent regime it ∝ velocity².

It defines relation between pressure drop and flow rate for viscous, laminar flow in pipes.

The actual discharge depends on the orifice area, head, and coefficient of discharge.

At high Reynolds numbers, inertial forces dominate viscous forces, creating turbulence.

Flow separates when the fluid decelerates against an increasing pressure region, leading to turbulence.

According to Bernoulli’s principle, as pressure energy drops, velocity energy rises

Venturi meters have high efficiency with minimal losses, giving Cd values close to 1.0.

It corrects for energy losses and gives the real discharge from theoretical calculations.

Darcy–Weisbach equation relates head loss to pipe length, diameter, flow velocity, and friction factor.

When fluid flows through a pipe, friction converts part of mechanical energy into heat, causing head loss.

The velocity and flow rate remain constant with time — hence steady flow.

As velocity increases at the throat, pressure decreases — a direct result of Bernoulli’s principle.

Venturimeter uses pressure difference between two points in a pipe to measure discharge.

It assumes fluid is non-viscous, incompressible, and flowing steadily without energy losses.

Total head is the sum of pressure energy, kinetic energy, and potential energy per unit weight.

The term p/ρg represents the pressure head or energy per unit weight due to pressure.

Bernoulli’s theorem states that the total energy (pressure + kinetic + potential) of a fluid remains constant along a streamline.

Streamlines show flow direction; equipotential lines show constant potential — hence, they intersect orthogonally.

Continuity ensures that mass flow rate into a control volume equals mass flow rate out.

At stagnation points, kinetic energy converts fully into pressure energy — velocity becomes zero.

Discharge or flow rate measures volume of fluid passing per second — hence cubic meter per second.

If both satisfy Laplace’s equation, it indicates potential flow that is both irrotational and incompressible.

Stream function is defined for 2D incompressible flow; its contours represent streamlines.

When inertial forces dominate over viscous forces, flow becomes chaotic — that’s turbulence.

In laminar flow, there’s no mixing between layers — they move in smooth, orderly paths.

Pathline represents the actual trajectory that a single particle follows in motion.

Velocity potential is valid only for irrotational flows — rotational flows do not satisfy its conditions.

In unsteady flow, the fluid velocity or other properties change over time at a fixed point.

Laminar flow occurs when viscous forces dominate, keeping fluid layers smooth and parallel.

The stream function defines streamlines — its constant value represents a streamline.

Velocity potential exists only for irrotational flows, where fluid elements do not rotate about their axis.

For incompressible flow, the product of area and velocity remains constant throughout the flow.

The continuity equation ensures the mass entering and leaving a control volume remains equal.

In uniform flow, velocity magnitude and direction remain same along the length of flow.

Steady flow means fluid properties like velocity remain constant with respect to time at a given point.

In steady flow, streamlines show the direction of fluid particles at every point in time.

Fluid kinematics focuses only on describing motion — velocity, acceleration, and flow type — not the forces behind them.

A piezometer is a simple vertical tube that indicates the pressure head at a point in fluid.

Archimedes’ principle defines buoyant force equal to the displaced fluid’s weight.

Deeper points in a fluid bear more pressure due to the weight of the liquid above.

A static fluid only resists normal stresses; any shear causes motion.

It shows pressure difference by comparing the heights of liquid columns in both limbs.

Positive metacentric height ensures the body returns to equilibrium after small tilts.

Pressure increases with depth, so the resultant acts below the centroid.

Pressure at depth h = ρgh, independent of shape or area of tank.

Archimedes’ principle states that a body immersed in fluid experiences an upward force equal to the weight of displaced fluid.

The centre of buoyancy is the centroid of the displaced volume of fluid.

The pressure difference equals the product of height difference and density difference.

Hydrostatic pressure always acts normal to the surface.

Centre of pressure is the point of action of the resultant hydrostatic force on a surface.

A barometer measures atmospheric pressure using a column of mercury.

Pressure head converts pressure into an equivalent column height of fluid.

Manometers use a column of liquid to measure small pressure differences with high accuracy.

Absolute pressure measures total pressure relative to perfect vacuum.

Pressure = Force/Area, and its SI unit is Pascal (Pa), equivalent to N/m².

In a fluid at rest, the pressure acts equally in all directions, as stated by Pascal’s Law.

Pressure in a static fluid increases linearly with depth due to the weight of the fluid above the point.

Capillary action occurs due to the combined effect of surface tension and adhesive forces.

Surface tension is the force per unit length acting along the surface of a liquid.

Newtonian fluids have a linear relationship between shear stress and velocity gradient.

Kinematic viscosity = Dynamic viscosity / Density, hence rearranging gives density.

Viscosity represents internal friction between fluid layers moving at different velocities.

Adhesion occurs when a liquid sticks to a solid surface — it causes wetting behavior.

A truly incompressible fluid can transmit pressure equally throughout its volume (Pascal’s Law).

Bernoulli’s principle relates pressure, velocity, and elevation for incompressible flow using energy conservation.

The continuity equation states that mass entering and leaving a control volume must remain constant.

In a static fluid, pressure is isotropic — acting equally in all directions.

An ideal fluid is a simplified concept used in theoretical analysis to neglect viscosity effects.

Dynamic viscosity quantifies internal resistance to flow, with its SI unit as N·s/m² (or Pa·s).

Kinematic viscosity relates the viscous forces to the fluid’s inertia and is expressed in m²/s.

Viscosity decreases with an increase in temperature for liquids, making flow easier.

Surface tension acts along the interface between liquid and air, causing capillary rise or depression.

Surface tension acts along the interface between liquid and air, causing capillary rise or depression.

Specific gravity is a pure ratio of densities, so it has no units.

An ideal fluid is theoretical — it cannot be compressed and has zero viscosity for simplified analysis.

Specific gravity compares the density of a fluid to that of water, making it dimensionless.

Viscosity measures a fluid’s internal resistance to motion or flow — higher viscosity means thicker flow.