- We consider fluids to be incompressible
- We assume that they have little or no internal friction or viscosity

### Streamline and turbulent flow

- The path followed by a small element of a moving fluid is called a line of flow.- A streamline is a curve whose tangent at any point is in the direction of the fluid velocity at that point.

A streamline flow occurs when all elements of a fluid passing a particular point follow the same path or line of flow as the elements that passed through that point previously.

- A streamline flow is achieved only when the speed is low.

- Turbulent flow generally occurs when the speed is high and where there are sharp bends along the path of the fluid.

### Equation of continuity

- Consider a fluid flowing (streamline flow) through a horizontal pipe with different crosssectional areas as shown.

**V1**and

**V2**respectively.

- The volume of fluid flowing per second in each section is given by;

**V = A L = A v t = A v.**Where

**L, v t**and

**v**is the distance moved in one second.

- Since the volumes in each section is the same, then,

**A1 V1 = A2 V2, hence A v = constant.**

- The above equation is known as the equation of continuity.

Since

**A1 > A2,**then

**V2 > V1.**i.e. the speed increases when a tube narrows.

- The quantity (A v) is called volume efflux i.e. volume flowing per second.

**Example 1**

A horizontal pipe of cross-sectional area 50 cm

^{2}carries water at the rate of 0.20 litres per second. Determine the speed:

a) Of the speed of water in the pipe.

b) When the tube narrows to 20 cm

^{2}at another point.

*Solution*

a) Volume efflux = 0.20 l per second = A v

From V (volume) = A v, then v = V / A = 0.20 × 10-3 / 50 x 10-4 = 0.04 m/s.

b) Since A1/v1 = A2/v2 then v2 = (0.05 x 0.04) / 0.02 = 0.1 m/s.