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cluponka [151]
3 years ago
9

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 botto

m of the step, what is its pressure at the top of the step?
Physics
1 answer:
sergejj [24]3 years ago
6 0

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.

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