Physics · Chapter 3
Study notes aligned to the official NEB syllabus.
A fluid is a substance that can flow from one place to another and takes the shape of its container; both liquids and gases are fluids. Fluid statics deals with fluids at rest: the pressure they exert, the up-thrust they provide, the surface effects at their boundaries, and the way they begin to move. This chapter covers Archimedes' principle and Pascal's law, buoyancy and floatation, surface tension and capillarity, viscosity, and the equations governing steady fluid flow (continuity and Bernoulli).
Pressure in a fluid at depth $h$ below the free surface of a liquid of density $\rho$ is:
$$P = h\rho g$$
This follows from the weight of a liquid column: $P = \dfrac{mg}{A} = \dfrac{(A h \rho)g}{A} = h\rho g$.
Relative density (specific gravity) is the ratio of the density of a substance to the density of water at $4^\circ\text{C}$; being a ratio, it has no unit.
Statement: When a body is wholly or partly immersed in a fluid at rest, it experiences an up-thrust (buoyant force) equal to the weight of the fluid displaced by the body.
$$U = V\rho g$$
where $V$ is the volume of fluid displaced and $\rho$ is the fluid density.
Statement: The pressure applied to an enclosed fluid at rest is transmitted equally and undiminished to every point of the fluid and to the walls of the container.
Pascal's law is the working principle of the hydraulic press, hydraulic brakes, and hydraulic lift. In a hydraulic press, a small force $F_1$ on a small piston of area $A_1$ produces a large force $F_2$ on a large piston of area $A_2$:
$$ \begin{aligned} & \frac{F_1}{A_1} = \frac{F_2}{A_2} \ \ & \Rightarrow\ \ & F_2 = F_1\frac{A_2}{A_1} \end{aligned} $$
Statement: A body floats in a fluid when the weight of the fluid displaced by its immersed part equals the total weight of the body.
$$W_{\text{body}} = U = V_{\text{immersed}},\rho_{\text{fluid}},g$$
For a body of volume $V$ and density $\rho_b$ floating with a fraction of its volume $V'$ immersed in a fluid of density $\rho_f$:
$$ \begin{aligned} & V\rho_b g = V'\rho_f g \ \ & \Rightarrow\ \ & \frac{V'}{V} = \frac{\rho_b}{\rho_f} \end{aligned} $$
The fraction of the volume submerged equals the ratio of the body's density to the fluid's density; this is why about $\tfrac{9}{10}$ of an iceberg lies below the water surface.
A fluid is a substance that can flow from one place to another and takes the shape of its container; both liquids and gases are fluids. Fluid statics deals with fluids at rest: the pressure they exert, the up-thrust they provide, the surface effects at their boundaries, and the way they begin to move. This chapter covers Archimedes' principle and Pascal's law, buoyancy and floatation, surface tension and capillarity, viscosity, and the equations governing steady fluid flow (continuity and Bernoulli).
Pressure in a fluid at depth below the free surface of a liquid of density is:
This follows from the weight of a liquid column: .
Relative density (specific gravity) is the ratio of the density of a substance to the density of water at ; being a ratio, it has no unit.
Statement: When a body is wholly or partly immersed in a fluid at rest, it experiences an up-thrust (buoyant force) equal to the weight of the fluid displaced by the body.
where is the volume of fluid displaced and is the fluid density.
Statement: The pressure applied to an enclosed fluid at rest is transmitted equally and undiminished to every point of the fluid and to the walls of the container.
Pascal's law is the working principle of the hydraulic press, hydraulic brakes, and hydraulic lift. In a hydraulic press, a small force on a small piston of area produces a large force on a large piston of area :
Statement: A body floats in a fluid when the weight of the fluid displaced by its immersed part equals the total weight of the body.
For a body of volume and density floating with a fraction of its volume immersed in a fluid of density :
The fraction of the volume submerged equals the ratio of the body's density to the fluid's density; this is why about of an iceberg lies below the water surface.