## Hydraulics

- Details
- Published: Sunday, 28 December 2014 11:24
- Written by Lance Hartley

### Pressure due to fluids

**Pressure** is a measure of the force acting over a specific area.

Downward pressure of a fluid in an open vessel is proportional to the **depth** of the fluid.

The downward pressure of a fluid in an open vessel is proportional to the **density** of the fluid.

The downward pressure of a fluid on the bottom of a vessel is independent of the shape of that vessel.

**Head** is the pressure exerted by the depth of water. One cubic metre of water contains 1000 litres. Each litre of water has a mass of one kilogram (kg). Therefore one cubic metre of water has a mass of 1000 kg.

**Note**: Each metre of head of water is equal to a pressure of 10 kPa.

The **rule of thumb** for allowing for height loss or gain is to: **add 10 kPa for every metre the nozzle is higher than the pump**, or **subtract 10 kPa for every metre the nozzle is lower than the pump**.

### Lift Using Air Pressure

A head of one metre equates to 10kPa. Therefore an atmospheric pressure of 100 kPa should be able to create a head of water of about 10 metres in theory.

For practical purposes, the maximum lift is approximately 7 to 8 metres.

A minus pressure of 30 kPa on the compound gauge would correspond to a lift of 3 metres because 1 metre of head / lift equals 10 kPa of pressure..

### Open Water Supply Capacity

Firefighters often have to determine the capacity of a water supply to estimate how long that supply will last.

**Consider a rectangular water tank, 6 m by 2½ m by 2 m**

Capacity in litres< /p>= length x width x depth x 1000 (multiply by 1000 to convert cubic metres to litres)

= 6 x 2½ x 2 x 1000= 6 x 2½ x 2 x1000 = 30 x 1000= 30000 litres.

**Consider a swimming pool**

Capacity (in litres) = length x breadth x depth x 1000 (multiply by 1000 to convert cubic metres to litres)

If it has an uneven depth, use the average depth in the calculation.

For example, a rectangular swimming pool is 4 metres wide, 8 metres long and is 1 metre deep at one end and 2 metres deep at the other.

Capacity (in litres) = length x width x depth x 1000

= 8 x 4 x (1+2) ÷ 2 x 1000

- = 8 x 4 x 1.5 x 1000

- = 48 x 1000

- = 48 000 litres.

If you required, say, a total water supply of 2000 L/min to fight a particular fire, this pool would supply that rate of flow for up to 24 minutes.(48 000 L ÷ 2000 L / min = 24 min) .

**Consider a cylindrical water tank**

Capacity (in litres) = 0.8 x depth x (diameter)^{2} x 1000

For example, a cylindrical water tank (standing on end) is 3 metres deep and 4 metres in diameter.

Capacity (in litres) = (pi x d^{2} x h)/4 (pi / 4 approximates to 0.8), therefore

= 0.8 x 3 m x (4m x 4m) x 1000

= 0.8 x 3 m x 16 m^{2} x 1000

= 0.8 x 48 m^{3 }x 1000

= 38.4 m^{3 }x 1000

= 38 400 litres

**Consider a flowing source**

Firefighters often underestimate the water supply available from quite small streams. For example, consider a creek that has a depth of 0.5 metres, a width of 4 metres and flowing past at a speed of 5 metres per minute.

Rate of flow (litres per minute) = depth x width x speed of flow x 1000

= 0.5 x 4 x 5 x 1000

= 0.5 x 20 x 1000

= 10 x 1000

= 10 000 L / min.

Questions

A nozzle is discharging water at 200 litres per minute. **How long will it take to empty a full tank of water** measuring 3 metres x 2 metres x 1 metre? (30 minutes)