Explanation Given information: When the diameter of the hose nozzle is 1.80 cm , the water splashes on the ground a distance of 0.950 m . Constricted diameter of the nozzle is 0.750 cm . Formula to calculate the velocity of the water, in the case of 1.80 cm diameter hose nozzle is, v = 2 g h v is the velocity of the water coming out from the pipe, in the case of 1.80 cm diameter hose nozzle. g is the acceleration due to gravity. h is the height at which the hose nozzle is held. Consider the equation of motion for the water from the nozzle exit to the ground. v − v 0 = g t t is the time taken by the water to hit the ground. v 0 is the initial velocity of water which is equal to 0. Substitute 0 for v 0 and ( 2 g h ) for v in the above equation to find t . 2 g h = g t t = 2 h g Formula to calculate the horizontal distance travelled by the water, in the case of 1.80 cm diameter hose nozzle is, s = v t v = s t (I) s is the horizontal distance travelled by the water, in the case 1.80 cm diameter hose nozzle. The flow rate of the water in both the case remains same, as the source remains same. Formula to calculate the horizontal distance travelled by the water, in the case of 7.50 cm diameter hose nozzle is, s ′ = v ′ t (II) s ′ is the horizontal distance travelled by the water, in the case 0 .750 cm diameter hose nozzle. v ′ is the velocity of the water coming out from the pipe, in the case of 0 .750 cm diameter hose nozzle, The flow rate of the water in both the case remains same, as the source remains same. Apply continuity equation for the flow of water through the nozzle in both cases. a v = a ′ v ′ (III) a is the cross-section area of 1.80 cm diameter hose nozzle. a ′ is the cross-section area of 0 .750 cm diameter hose nozzle. Cross section area of the nozzle is proportional to the square of its diameter. Therefore, a ∝ d 2 a = k d 2 k is proportionality constant

University Physics with Modern Physics, Volume 2 (Chs. 21-37); Mastering Physics with Pearson eText -- ValuePack Access Card (14th Edition)

14th Edition

ISBN: 9780134265414

Author: Hugh D. Young, Roger A. Freedman

Publisher: PEARSON

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Variation of pressure

From the equation of pressure, pressure is directly proportional to the applied force.

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Chapter 12, Problem 12.79P

To determine

The distance from the nozzle to the point in the ground, where the water hits, when the diameter of the nozzle is 0.750 cm.

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Chapter 12, Problem 12.78P

Chapter 12, Problem 12.80P

Chapter 12 Solutions

University Physics with Modern Physics, Volume 2 (Chs. 21-37); Mastering Physics with Pearson eText -- ValuePack Access Card (14th Edition)

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The distance from the nozzle to the point in the ground, where the water hits, when the diameter of the nozzle is 0.750 cm .

Solution Summary: The author calculates the distance from the nozzle to the point in the ground, where the water hits.

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The distance from the nozzle to the point in the ground, where the water hits, when the diameter of the nozzle is 0.750 cm.

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Chapter 12 Solutions