Question

Water flows with constant speed through a garden hose that goes up to 27.5 cm high. if the water pressure is 132kpa at the bottom of the step, what is its pressure at the top of the step?

Answer 1

Answer:

The pressure at the top of the step is 129.303 kilopascals.

Explanation:

From Hydrostatics we find that the pressure difference between extremes of the water column is defined by the following formula, which is a particular case of the Bernoulli's Principle ($v_{bottom}\approx v_{top}$):

$p_{bottom}-p_{top} = \rho\cdot g\cdot \Delta h$ (1)

$p_{bottom}$, $p_{top}$ - Total pressures at the bottom and at the top, measured in pascals.

$\rho$ - Density of the water, measured in kilograms per cubic meter.

$\Delta h$ - Height difference of the step, measured in meters.

If we know that $p_{bottom} = 132000\,Pa$, $\rho = 1000\,\frac{kg}{m^{3}}$, $g = 9.807\,\frac{m}{s^{2}}$ and $\Delta h = 0.275\,m$, then the pressure at the top of the step is:

$p_{top} = p_{bottom}-\rho\cdot g\cdot \Delta h$

$p_{top} = 132000\,Pa-\left(1000\,\frac{kg}{m^{3}} \right)\cdot \left(9.807\,\frac{m}{s^{2}} \right)\cdot (0.275\,m)$

$p_{top} = 129303.075\,Pa$

$p_{top} = 129.303\,kPa$

The pressure at the top of the step is 129.303 kilopascals.

Answer 2

The pressure of the water at the top of the step is 1.293 x 10⁵ Pa.

The given parameters:

• Height of the hose, h = 27.5 cm = 0.275 m
• Pressure of the water at bottom, Pb = 132 kPa

The pressure of the water at the top of the step is calculated as follows;

$P_b - P_t = \rho gh\\\\P_t = P_b - \rho gh$

where;

$\rho$ is the density of the water

$P_t = (132,000 \ Pa) \ - \ (1000 \times 9.8 \times 0.275)\\\\P_t = 1.293 \times 10^5 \ Pa$

Thus, the pressure of the water at the top of the step is 1.293 x 10⁵ Pa.

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