Question

the water level in a tank is 20 m above the ground. a hose is connected to the bottom of the tank, and the nozzle at the end of the hose is pointed straight up. the tank cover is airtight, and the air pressure above the water surface is 2 atm gage. the system is at sea level. determine the maximum height to which the water stream could rise

Answer 1

The maximum height of the water stream that could rise is 40.65 m. It can be calculated using Principle of Bernoulli.

Principle of Bernoulli can be described an increase in the speed of a fluid happen simultaneously with a decrease in pressure or a decrease in the fluid's potential energy. Equation of Bernoulli is shown as a conservation of energy law for a flowing fluid. Bernoulli equation is shown below:

$P_1$/ρg + $v_1$²/2g + $h_1$  = $P_2$/ρg +$v_2$²/2g + $h_2$

Where:

ρ = fluid density

g = acceleration due to gravity

$P_1$ = pressure at elevation 1

$v_1$ = velocity at elevation 1

$h_1$ = height of elevation 1

$P_2$ = pressure at elevation 2

$v_2$ = velocity at elevation 2

$h_2$ = height at elevation 2

Assumed that the water at free surface, so $v_1 = v_2$ = 0

So, the formula will be

$P_1$/ρg + $h_1$  = Patm/ρg + $h_2$

Based on the scenario, we know that:

$h_1$ = 20 m

$P_1$gage = 2 atm ≈ 20265 N/m

ρ = 1000 kg/m²

From the scenario, we will determine the maximum height by using the equation of bernoulli and it will be

$h_2$ = ($P_1$ - Patm)/ρg + $Z_1$

$h_2$ = $\frac{2 atm}{1000(9.81)}$ x $(\frac{101325N/m^{2} }{1 atm} )(\frac{1 kg.m/s^{2} }{1 N} )$ + 20 = 40.65 m

So, from that, we can conclude the maximum height of the water stream that could rise is 40.65 m.

Learn more about bernoulli principle at brainly.com/question/15415820

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