Fluids

---

A fluid is a liquid, gas, or other material that may continuously move or flow under an applied shear force, or external force. They are substances which cannot resist any shear force applied to them.

---

---

---

Pressure

---

Prerequesite

---

Describing Pressure

$$\text{Pressure}=\frac{\text{Force}}{\text{Area}}$$

or

$$P=\frac{F}{A}$$

• where
• $P$ is the pressure on a surface in pascals, $\mathit{Pa}$;
• $F$ is the force applied perpendicular to the surface in newtons, $N$;
• and
• $A$ is the area of the surface in square metres, $m^2$.

---

The rearrangements:

---

Questions:

Pressure Video

Practice Questions

Textbook Exercise

(Care of corbettmaths.com)

---

Follow on reading

Mechanical Stress
(Care of www.savemyexams.com)

---

Further reading:

Pascals principle
(Care of en.wikipedia.org)

Pressure at Depth in a Liquid

Young's Modulus
(Care of en.wikipedia.org)

---

Viscosity

Viscosity is a physical property of fluids. It shows resistance of the fluid to flow. In a simple example, water has a low viscosity, as it is "thin". Syrup and tar, on the other hand, have a high viscosity, as they are "thick". A way to test for viscosity is the speed at which the substance runs down a slope. Syrup would reach the bottom very slowly, and water would be much quicker.
(See simple.wikipedia.org/wiki/Viscosity for more)

---

Stokes' Law

Stokes' Law is an empirical law for the drag force exerted on a small spherical object moving slowly through a viscous fluid.

$$F=6\mathrm{\pi }\eta rv$$

• where
• $F$ is the drag force on a sphere in newton, $N$,
• $\eta$ is the viscosity of the fuild the sphere is falling through,
• $r$ is the radius of the sphere in metres, $m$
• and
• $v$ is the velocity of the sphere through the fluid in metres per second, $m/s$.

This equation is only valid for small spheres at low speed with laminar flow (i.e., without turbulent flow).

In general, the visocity of a fluid depends on the temperature. Most fluids become less viscose as the temperature increased.

---

---

States of Matter

These are three of the four classical states of matter. The fourth is Plasma.

---

Heat and Temperature

---

Specific Heat Capacity

$$\Delta E=mc\Delta \theta$$

• where
• $\Delta E$ is the change in internal energy (joule, J);
• $m$ is the mass of the material (kilogram, kg);
• $c$ is the specific heat capacity (joules per kilogram per kelvin, Jkg^-1K^-1);
• and
• $\Delta \theta$ is the change in temperature (kelvin, K).

Each state of matter has a different value of specific heat capacity for each type of material

---

Latent Heat
of fusion and vapourisation

$$\Delta E=mL$$

• where
• $\Delta E$ is the change in internal energy during a state change (joules, J);
• $m$ is the mass of material changing state in kg;
• and
• $L$ is the latent heat of fusion, $L_f$ or vapourisation, $L_v$ (joules per kilogram, $\text{J}{\text{kg}}^{-1}$).

The latent heat has different value for each state change and for each material.

---

Gas Laws

for a fixed mass of gas

• where
• $p$ is the gas pressure in pascals, Pa;
• $V$ is the volume of the gas in cubic metres, $m^3$;
• and
• $T$ is the temperature of the gas in kelvin, K.

For a given amount of gas we can consider situations before (1) and after (2) a change

$$\frac{p_1{V}_1}{T_1}=\frac{p_2{V}_2}{T_2}$$

... search for GCSE Boyle's Law Questions ..

---

Ideal Gas Law

$$pV=nRT$$ $$pV=NkT$$ $$\Rightarrow nR=Nk$$

If $N=N_A$, then $n=1$, so

$$k=\frac{R}{N_A}$$

---

Brownian Motion

---

$$pV=\frac{1}{3}Nm<c^2>$$

Kinetic Theory of Gases - Assumptions:

• Large number of particles;
• particles are in continuous, rapid, random motion;
• All collisions are elastic;
• Volume of particles is negligible compared to the volume of the container;
• there are no intermolecular forces except when particles collide;
• collision times are negligible compared to the time of flight.

For each assumption remember the supporting evidence.

Density form of the kinetic model equation

$$p=\frac{1}{3}\rho {\left(c_{\text{RMS}}\right)}^2$$

---

Pressure at Depth in a Liquid

$p=\rho gh$

• where
• $p$ is the pressure in pascals, $Pa$;
• $\rho$ is the density in kilograms per cubic metre, $kg{m}^{-3}$;
• $g$ is the gravitational field strength in metres per second squared, $m{s}^{-2}$;
• and
• $h$ is the height in metres, $m$.

---