Question

Fire hoses used in major structural fires have an inside diameter of 6.40 cm (figure 6) Suppose such a hose carries a flow of 46.0 x 10-3 m3/s, starting at a gauge pressure of 1.32×106 N/m2. The hose rises up 10.0 m along a ladder to a nozzle having an inside diameter of 4.00 cm. Determine the pressure in the nozzle

Answer 1

Explanation:

OpenStax-CNX module: m42208 1

The Most General Applications of

Bernoulli's Equation*

OpenStax

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Abstract

• Calculate using Torricelli's theorem.

• Calculate power in uid ow.

1 Torricelli's Theorem

Figure 4 shows water gushing from a large tube through a dam. What is its speed as it emerges? Interestingly,

if resistance is negligible, the speed is just what it would be if the water fell a distance h from the surface of

the reservoir; the water's speed is independent of the size of the opening. Let us check this out. Bernoulli's

equation must be used since the depth is not constant. We consider water owing from the surface (point

1) to the tube's outlet (point 2). Bernoulli's equation as stated in previously is

P1 +

1

2

ρv

2

1 + ρgh1 = P2 +

1

2

ρv

2

2 + ρgh2

. (1)

Both P1 and P2 equal atmospheric pressure (P1 is atmospheric pressure because it is the pressure at the top

of the reservoir. P2 must be atmospheric pressure, since the emerging water is surrounded by the atmosphere

and cannot have a pressure dierent from atmospheric pressure.) and subtract out of the equation, leaving

1

2

ρv

2

1 + ρgh1 =

1

2

ρv

2

2 + ρgh2

. (2)

Solving this equation for v

2

2

, noting that the density ρ cancels (because the uid is incompressible), yields

v

2

2 = v

2

1 + 2g (h1 − h2). (3)

We let h = h1 − h2; the equation then becomes

v

2

2 = v

2

1 + 2gh (4)