☰ Contents · Physics

Pressure and speed in technology

Lessons 21 · 1 lessons · N. Sh. Turdiyev, K. A. Tursunmetov, A. G. Ganiyev, K. T. Suyarov, J. E. Usarov, A. K. Avliyoqulov. Physics Grade 10, 1st edition. Niso Poligraf Publishing House, Tashkent, 2017
21

Using the dependence of pressure on speed in moving gases and liquids in technology

Textbook: pp. 71–74
GoalExplain how Bernoulli’s law appears in technology and nature (wing lift, the Magnus effect, Torricelli’s formula).
New words
dynamic pressure · dinamik bosimlift force · ko‘taruvchi kuchMagnus effect · Magnus effektiTorricelli’s formula · Torrichelli formulasi
Explanation

In a moving gas or liquid the pressure is lower where the speed is higher. If you blow between two vertically held sheets of paper, the air between them speeds up and its pressure drops, so the outer pressure pushes the sheets together. An aircraft wing is shaped so that the air passes faster over its upper side; the pressure above is lower than below, and the pressure difference gives an upward lift force. Air around a spinning ball or cylinder moves faster on one side than on the other, and the pressure difference deflects it sideways – the Magnus effect (a curving kick in football). For a hole at depth h below the surface in an open vessel, Bernoulli’s equation gives υ = √(2gh) (Torricelli’s formula): the speed equals that of a body falling freely through h. The same law underlies the spray bottle, the carburettor and the Venturi tube.

Worked examples
A vessel has a hole 3.2 m below the water level (g = 10 m/s²): υ = √(2·10·3.2) = √64 = 8 m/s. If the depth grows 4 times, the speed grows 2 times.
An aircraft wing has an area of 20 m² and the pressure difference below and above it is 1500 Pa. The lift is F = Δp·S = 1500·20 = 30 000 N = 30 kN, equal to the weight of a 3000 kg load (g = 10 m/s²).
Class activity

Only in class with the teacher: hold two sheets of paper 3–4 cm apart, blow gently between them and explain why they come together. Do not do it near an open window or other people.

Practice
1
How is the lift of an aircraft wing produced?
2
The hole is 1.25 m below the water level (g = 10 m/s²). What is the speed υ = √(2gh) in m/s?
3
The wing area is 12 m², the pressure difference 2000 Pa. What is the lift (N)?
4
What is the Magnus effect and where does it appear?