Fundamentals of Thermal‐Fluid Sciences

Applications of the Bernoulli Equation

[NTC २०७४/१२/११ ]

Q. Water is flowing from a garden hose (Fig. 12–18). A man places his thumb to cover most of the hose outlet, causing a thin jet of high-speed water to emerge. The pressure in the hose just upstream of his thumb is 400 kPa. If the hose is held upward, what is the maximum height that the jet could achieve?[10Marks]

FIGURE 12–18

Solution:

Assumptions:

1. The flow exiting into the air is steady, incompressible, and irrotational.

2. The water pressure in the hose near the outlet is equal to the main water pressure.

3. The surface tension effects are negligible.

4. The friction between the water and air is negligible

5. The irreversibilities that may occur at the outlet of the hose due to abrupt expansion are negligible.

Constants: 

ρwater = 1000 kg/m3 

Calculations:

The water height will be at a maximum under the assumptions. The water velocity in the hose is relatively low (V1 = 0) and we take the hose outlet as the reference level (z1 = 0). At the top of the water trajectory, the velocity reaches zero (V2 = 0) and atmospheric pressure pertains.

   Therefore, the water jet can rise as high as 40.8 m into the sky in this case.

Discussion The result obtained by the Bernoulli equation represents the upper limit and should be interpreted accordingly. It tells us that the water cannot possibly rise more than 40.8 m, and, in all likelihood, the rise will be much less than 40.8 m due to irreversible losses that we neglected.