Fluid Mechanics · Unit 1 · Lesson 2 of 13

What Does Fluid Mechanics Study?

Introduction to fluid mechanics 7 min

Curiosity question

Your heart, a car's brakes, an aeroplane wing and the AC in your room all depend on the same subject. Which one, and what does it actually study?

1. Real-World Problem

A housing society's pump must send water from an underground sump to a tank on a five-storey roof. Before choosing a pump, an engineer asks: how hard will the water push, how fast must it flow, and how much energy will it need?

2. Predict

Make your guess before you try the experiment. You will see the answer after the next step.

Predict

The air in a closed room is perfectly still. Is it part of fluid mechanics?

3. Experiment

Tap each glowing hotspot in the street scene. For each one, read which fluid is working there and the question fluid mechanics answers about it. Try to find all 8.

Tag each hotspot as "How hard does it push?", "Where and how fast does it flow?" or "How much energy?". On the roof tank, drag the water level to 10 m above the tap and read the gauge: you will use that number in Validate.

4. Understand

Fluid mechanics is the branch of mechanics that studies fluids (liquids and gases) at rest and in motion, and the forces they exert. It uses the same laws as the rest of mechanics: Newton's laws of motion, conservation of mass and conservation of energy.

It answers three kinds of questions:

  • How hard does the fluid push? Pressure on a dam, on a submarine, inside a tyre.
  • Where and how fast does it flow? Water through pipes, air over a wing.
  • How much energy does it carry or need? A pump lifting water, a turbine making electricity.

The quantities it works with most: density, pressure, velocity, viscosity and temperature.

5. Derive

Step 1. Density is mass per unit volume; pressure is the normal force per unit area:

\rho = \frac{m}{V} \qquad p = \frac{F_n}{A}

ρ is density (kg/m³), m mass (kg), V volume (m³); p is pressure (Pa), F_n the force pushing straight onto a surface (N), A the area (m²).

Step 2. Take a column of still water of height h standing on area A. Its mass is m = ρV = ρAh, so its weight is F = mg = ρAhg.

Step 3. That weight presses on the area A, so the extra pressure at the bottom is:

p = \frac{F}{A} = \frac{\rho A h g}{A} = \rho g h

g = 9.81 m/s². This is gauge pressure (pressure above the atmosphere). Lesson 6 builds on it.

6. Calculate

  • A 2 L bottle of cooking oil has a mass of 1.76 kg. V = 2 L = 0.002 m³, so ρ = 1.76 ÷ 0.002 = 880 kg/m³.
  • A water tank is filled 1 m deep. Gauge pressure at its floor: p = 1000 × 9.81 × 1 = 9810 Pa, about 9.8 kPa.
  • A tap 10 m below the tank's water surface, with no water flowing: p = 1000 × 9.81 × 10 = 98,100 Pa, about 98 kPa (close to 1 bar).

7. Apply

  • Building water supply: tank height decides tap pressure.
  • Weather forecasts: the atmosphere is a fluid in motion.
  • Medicine: blood flow, inhalers, ventilators.
  • Sport: a cricket ball swings because of how air flows around its seam.
  • Aviation: wings, jet engines, cabin pressure.

8. Validate

On the map's roof tank, set the water level 10 m above the tap: the gauge must read about 98 kPa. Where p = ρgh applies: still water only. When the tap is open, the reading drops, because some pressure turns into flow speed and some is lost to friction in the pipes (Lessons 6 and 13).

Easy To Mix Up

  • Fluid mechanics is not only about water. Air and other gases are a big part of it.
  • It is not only about motion. Fluids at rest (a dam, a water tank) are part of it too.
  • Density is mass per volume, not weight per volume (that is specific weight, ρg, in N/m³).

9. Quiz

Four quick questions: a concept, a calculation and an interpretation. Each answer comes with an explanation. Score 3 or more to mark this lesson completed.

Check Your Understanding

Four questions: a concept, a calculation and an interpretation. Every answer comes with an explanation. Score 3 of 4 to mark the lesson completed.

Up next

People were using fluid mechanics more than 4,000 years before anyone wrote its equations. Who worked it out?

Go to Lesson 3: Who Figured Out How Fluids Behave? →

Read More

  • Cengel and Cimbala, "Introduction and Basic Concepts" (application areas) and "Pressure and Fluid Statics".
  • NPTEL, Introduction to Fluid Mechanics (Prof. Suman Chakraborty, IIT Kharagpur): Weeks 1 and 4.