Explanation Given : v = 〈 x − y , z + y + 4 , z 2 〉 , net given by y = 1 − x 2 − z 2 , y ≥ 0 oriented in the positive y-direction Calculation : Step 1: Since in the positive y direction , y=0 x 2 + z 2 = 1 Step 2: Water flow = ∫ ∫ S V d S Normal vector to S is n ^ = j d S = d x d z | n . j | = d x d z Step 3: Water flow= ∫ ∫ x 2 + z 2 − 1 V ...

4th Edition

ISBN: 9781319323394

Author: Rogawski

Publisher: MAC HIGHER

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Question

Chapter 17.5, Problem 27E

To determine

To calculate: The flow rate of water across the net given by $y = \sqrt{1 - x^{2} - z^{2}}, y \geq 0$ oriented in the positive y-direction if the velocity vector field for the river is given by $v = 〈 x - y, z + y + 4, z^{2} 〉$

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Chapter 17.5, Problem 26E

Chapter 17.5, Problem 28E

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Chapter 17 Solutions

CALCULUS W/SAPLING ACCESS >IC<

Ch. 17.1 - Prob. 1PQ Ch. 17.1 - Prob. 2PQ Ch. 17.1 - Prob. 3PQ Ch. 17.1 - Prob. 4PQ Ch. 17.1 - Prob. 1E Ch. 17.1 - Prob. 2E Ch. 17.1 - Prob. 3E Ch. 17.1 - Prob. 4E Ch. 17.1 - Prob. 5E Ch. 17.1 - Prob. 6E

Ch. 17.1 - Prob. 7E Ch. 17.1 - Prob. 8E Ch. 17.1 - Prob. 9E Ch. 17.1 - Prob. 10E Ch. 17.1 - Prob. 11E Ch. 17.1 - Prob. 12E Ch. 17.1 - Prob. 13E Ch. 17.1 - Prob. 14E Ch. 17.1 - Prob. 15E Ch. 17.1 - Prob. 16E Ch. 17.1 - Prob. 17E Ch. 17.1 - Prob. 18E Ch. 17.1 - Prob. 19E Ch. 17.1 - Prob. 20E Ch. 17.1 - Prob. 21E Ch. 17.1 - Prob. 22E Ch. 17.1 - Prob. 23E Ch. 17.1 - Prob. 24E Ch. 17.1 - Prob. 25E Ch. 17.1 - Prob. 26E Ch. 17.1 - Prob. 27E Ch. 17.1 - Prob. 28E Ch. 17.1 - Prob. 29E Ch. 17.1 - Prob. 30E Ch. 17.1 - Prob. 31E Ch. 17.1 - Prob. 32E Ch. 17.1 - Prob. 33E Ch. 17.1 - Prob. 34E Ch. 17.1 - Prob. 35E Ch. 17.1 - Prob. 36E Ch. 17.1 - Prob. 37E Ch. 17.1 - Prob. 38E Ch. 17.1 - Prob. 39E Ch. 17.1 - Prob. 40E Ch. 17.1 - Prob. 41E Ch. 17.1 - Prob. 42E Ch. 17.1 - Prob. 43E Ch. 17.1 - Prob. 44E Ch. 17.1 - Prob. 45E Ch. 17.1 - Prob. 46E Ch. 17.1 - Prob. 47E Ch. 17.1 - Prob. 48E Ch. 17.1 - Prob. 49E Ch. 17.1 - Prob. 50E Ch. 17.1 - Prob. 51E Ch. 17.1 - Prob. 52E Ch. 17.1 - Prob. 53E Ch. 17.1 - Prob. 54E Ch. 17.1 - Prob. 55E Ch. 17.1 - Prob. 56E Ch. 17.1 - Prob. 57E Ch. 17.2 - Prob. 1PQ Ch. 17.2 - Prob. 2PQ Ch. 17.2 - Prob. 3PQ Ch. 17.2 - Prob. 4PQ Ch. 17.2 - Prob. 1E Ch. 17.2 - Prob. 2E Ch. 17.2 - Prob. 3E Ch. 17.2 - Prob. 4E Ch. 17.2 - Prob. 5E Ch. 17.2 - Prob. 6E Ch. 17.2 - Prob. 7E Ch. 17.2 - Prob. 8E Ch. 17.2 - Prob. 9E Ch. 17.2 - Prob. 10E Ch. 17.2 - Prob. 11E Ch. 17.2 - Prob. 12E Ch. 17.2 - Prob. 13E Ch. 17.2 - Prob. 14E Ch. 17.2 - Prob. 15E Ch. 17.2 - Prob. 16E Ch. 17.2 - Prob. 17E Ch. 17.2 - Prob. 18E Ch. 17.2 - Prob. 19E Ch. 17.2 - Prob. 20E Ch. 17.2 - Prob. 21E Ch. 17.2 - Prob. 22E Ch. 17.2 - Prob. 23E Ch. 17.2 - Prob. 24E Ch. 17.2 - Prob. 25E Ch. 17.2 - Prob. 26E Ch. 17.2 - Prob. 27E Ch. 17.2 - Prob. 28E Ch. 17.2 - Prob. 29E Ch. 17.2 - Prob. 30E Ch. 17.2 - Prob. 31E Ch. 17.2 - Prob. 32E Ch. 17.2 - Prob. 33E Ch. 17.2 - Prob. 34E Ch. 17.2 - Prob. 35E Ch. 17.2 - Prob. 36E Ch. 17.2 - Prob. 37E Ch. 17.2 - Prob. 38E Ch. 17.2 - Prob. 39E Ch. 17.2 - Prob. 40E Ch. 17.2 - Prob. 41E Ch. 17.2 - Prob. 42E Ch. 17.2 - Prob. 43E Ch. 17.2 - Prob. 44E Ch. 17.2 - Prob. 45E Ch. 17.2 - Prob. 46E Ch. 17.2 - Prob. 47E Ch. 17.2 - Prob. 48E Ch. 17.2 - Prob. 49E Ch. 17.2 - Prob. 50E Ch. 17.2 - Prob. 51E Ch. 17.2 - Prob. 52E Ch. 17.2 - Prob. 53E Ch. 17.2 - Prob. 54E Ch. 17.2 - Prob. 55E Ch. 17.2 - Prob. 56E Ch. 17.2 - Prob. 57E Ch. 17.2 - Prob. 58E Ch. 17.2 - Prob. 59E Ch. 17.2 - Prob. 60E Ch. 17.2 - Prob. 61E Ch. 17.2 - Prob. 62E Ch. 17.2 - Prob. 63E Ch. 17.2 - Prob. 64E Ch. 17.2 - Prob. 65E Ch. 17.2 - Prob. 66E Ch. 17.2 - Prob. 67E Ch. 17.2 - Prob. 68E Ch. 17.2 - Prob. 69E Ch. 17.2 - Prob. 70E Ch. 17.2 - Prob. 71E Ch. 17.2 - Prob. 72E Ch. 17.2 - Prob. 73E Ch. 17.2 - Prob. 74E Ch. 17.2 - Prob. 75E Ch. 17.3 - Prob. 1PQ Ch. 17.3 - Prob. 2PQ Ch. 17.3 - Prob. 3PQ Ch. 17.3 - Prob. 4PQ Ch. 17.3 - Prob. 1E Ch. 17.3 - Prob. 2E Ch. 17.3 - Prob. 3E Ch. 17.3 - Prob. 4E Ch. 17.3 - Prob. 5E Ch. 17.3 - Prob. 6E Ch. 17.3 - Prob. 7E Ch. 17.3 - Prob. 8E Ch. 17.3 - Prob. 9E Ch. 17.3 - Prob. 10E Ch. 17.3 - Prob. 11E Ch. 17.3 - Prob. 12E Ch. 17.3 - Prob. 13E Ch. 17.3 - Prob. 14E Ch. 17.3 - Prob. 15E Ch. 17.3 - Prob. 16E Ch. 17.3 - Prob. 17E Ch. 17.3 - Prob. 18E Ch. 17.3 - Prob. 19E Ch. 17.3 - Prob. 20E Ch. 17.3 - Prob. 21E Ch. 17.3 - Prob. 22E Ch. 17.3 - Prob. 23E Ch. 17.3 - Prob. 24E Ch. 17.3 - Prob. 25E Ch. 17.3 - Prob. 26E Ch. 17.3 - Prob. 27E Ch. 17.3 - Prob. 28E Ch. 17.3 - Prob. 29E Ch. 17.3 - Prob. 30E Ch. 17.3 - Prob. 31E Ch. 17.3 - Prob. 32E Ch. 17.3 - Prob. 33E Ch. 17.3 - Prob. 34E Ch. 17.3 - Prob. 35E Ch. 17.4 - Prob. 1PQ Ch. 17.4 - Prob. 2PQ Ch. 17.4 - Prob. 3PQ Ch. 17.4 - Prob. 4PQ Ch. 17.4 - Prob. 5PQ Ch. 17.4 - Prob. 6PQ Ch. 17.4 - Prob. 1E Ch. 17.4 - Prob. 2E Ch. 17.4 - Prob. 3E Ch. 17.4 - Prob. 4E Ch. 17.4 - Prob. 5E Ch. 17.4 - Prob. 6E Ch. 17.4 - Prob. 7E Ch. 17.4 - Prob. 8E Ch. 17.4 - Prob. 9E Ch. 17.4 - Prob. 10E Ch. 17.4 - Prob. 11E Ch. 17.4 - Prob. 12E Ch. 17.4 - Prob. 13E Ch. 17.4 - Prob. 14E Ch. 17.4 - Prob. 15E Ch. 17.4 - Prob. 16E Ch. 17.4 - Prob. 17E Ch. 17.4 - Prob. 18E Ch. 17.4 - Prob. 19E Ch. 17.4 - Prob. 20E Ch. 17.4 - Prob. 21E Ch. 17.4 - Prob. 22E Ch. 17.4 - Prob. 23E Ch. 17.4 - Prob. 24E Ch. 17.4 - Prob. 25E Ch. 17.4 - Prob. 26E Ch. 17.4 - Prob. 27E Ch. 17.4 - Prob. 28E Ch. 17.4 - Prob. 29E Ch. 17.4 - Prob. 30E Ch. 17.4 - Prob. 31E Ch. 17.4 - Prob. 32E Ch. 17.4 - Prob. 33E Ch. 17.4 - Prob. 34E Ch. 17.4 - Prob. 35E Ch. 17.4 - Prob. 36E Ch. 17.4 - Prob. 37E Ch. 17.4 - Prob. 38E Ch. 17.4 - Prob. 39E Ch. 17.4 - Prob. 40E Ch. 17.4 - Prob. 41E Ch. 17.4 - Prob. 42E Ch. 17.4 - Prob. 43E Ch. 17.4 - Prob. 44E Ch. 17.4 - Prob. 45E Ch. 17.4 - Prob. 46E Ch. 17.4 - Prob. 47E Ch. 17.4 - Prob. 48E Ch. 17.4 - Prob. 49E Ch. 17.4 - Prob. 50E Ch. 17.4 - Prob. 51E Ch. 17.5 - Prob. 1PQ Ch. 17.5 - Prob. 2PQ Ch. 17.5 - Prob. 3PQ Ch. 17.5 - Prob. 4PQ Ch. 17.5 - Prob. 5PQ Ch. 17.5 - Prob. 6PQ Ch. 17.5 - Prob. 7PQ Ch. 17.5 - Prob. 1E Ch. 17.5 - Prob. 2E Ch. 17.5 - Prob. 3E Ch. 17.5 - Prob. 4E Ch. 17.5 - Prob. 5E Ch. 17.5 - Prob. 6E Ch. 17.5 - Prob. 7E Ch. 17.5 - Prob. 8E Ch. 17.5 - Prob. 9E Ch. 17.5 - Prob. 10E Ch. 17.5 - Prob. 11E Ch. 17.5 - Prob. 12E Ch. 17.5 - Prob. 13E Ch. 17.5 - Prob. 14E Ch. 17.5 - Prob. 15E Ch. 17.5 - Prob. 16E Ch. 17.5 - Prob. 17E Ch. 17.5 - Prob. 18E Ch. 17.5 - Prob. 19E Ch. 17.5 - Prob. 20E Ch. 17.5 - Prob. 21E Ch. 17.5 - Prob. 22E Ch. 17.5 - Prob. 23E Ch. 17.5 - Prob. 24E Ch. 17.5 - Prob. 25E Ch. 17.5 - Prob. 26E Ch. 17.5 - Prob. 27E Ch. 17.5 - Prob. 28E Ch. 17.5 - Prob. 29E Ch. 17.5 - Prob. 30E Ch. 17.5 - Prob. 31E Ch. 17.5 - Prob. 32E Ch. 17.5 - Prob. 33E Ch. 17.5 - Prob. 34E Ch. 17.5 - Prob. 35E Ch. 17.5 - Prob. 36E Ch. 17.5 - Prob. 37E Ch. 17.5 - Prob. 38E Ch. 17 - Prob. 1CRE Ch. 17 - Prob. 2CRE Ch. 17 - Prob. 3CRE Ch. 17 - Prob. 4CRE Ch. 17 - Prob. 5CRE Ch. 17 - Prob. 6CRE Ch. 17 - Prob. 7CRE Ch. 17 - Prob. 8CRE Ch. 17 - Prob. 9CRE Ch. 17 - Prob. 10CRE Ch. 17 - Prob. 11CRE Ch. 17 - Prob. 12CRE Ch. 17 - Prob. 13CRE Ch. 17 - Prob. 14CRE Ch. 17 - Prob. 15CRE Ch. 17 - Prob. 16CRE Ch. 17 - Prob. 17CRE Ch. 17 - Prob. 18CRE Ch. 17 - Prob. 19CRE Ch. 17 - Prob. 20CRE Ch. 17 - Prob. 21CRE Ch. 17 - Prob. 22CRE Ch. 17 - Prob. 23CRE Ch. 17 - Prob. 24CRE Ch. 17 - Prob. 25CRE Ch. 17 - Prob. 26CRE Ch. 17 - Prob. 27CRE Ch. 17 - Prob. 28CRE Ch. 17 - Prob. 29CRE Ch. 17 - Prob. 30CRE Ch. 17 - Prob. 31CRE Ch. 17 - Prob. 32CRE Ch. 17 - Prob. 33CRE Ch. 17 - Prob. 34CRE Ch. 17 - Prob. 35CRE Ch. 17 - Prob. 36CRE Ch. 17 - Prob. 37CRE Ch. 17 - Prob. 38CRE Ch. 17 - Prob. 39CRE Ch. 17 - Prob. 40CRE Ch. 17 - Prob. 41CRE Ch. 17 - Prob. 42CRE Ch. 17 - Prob. 43CRE Ch. 17 - Prob. 44CRE Ch. 17 - Prob. 45CRE Ch. 17 - Prob. 46CRE Ch. 17 - Prob. 47CRE Ch. 17 - Prob. 48CRE Ch. 17 - Prob. 49CRE Ch. 17 - Prob. 50CRE Ch. 17 - Prob. 51CRE Ch. 17 - Prob. 52CRE Ch. 17 - Prob. 53CRE Ch. 17 - Prob. 54CRE Ch. 17 - Prob. 55CRE Ch. 17 - Prob. 56CRE Ch. 17 - Prob. 57CRE Ch. 17 - Prob. 58CRE Ch. 17 - Prob. 59CRE Ch. 17 - Prob. 60CRE Ch. 17 - Prob. 61CRE

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The flow rate of water across the net given by y = 1 − x 2 − z 2 , y ≥ 0 oriented in the positive y-direction if the velocity vector field for the river is given by v = 〈 x − y , z + y + 4 , z 2 〉

Solution Summary: The author calculates the flow rate of water across the net given by y = 1 x 2 z 2 and the velocity vector field for the river.

Videos

To calculate: The flow rate of water across the net given by $y = \sqrt{1 - x^{2} - z^{2}}, y \geq 0$ oriented in the positive y-direction if the velocity vector field for the river is given by $v = 〈 x - y, z + y + 4, z^{2} 〉$

Want to see the full answer?

Chapter 17 Solutions

The flow rate of water across the net given by y = 1 − x 2 − z 2 , y ≥ 0 oriented in the positive y-direction if the velocity vector field for the river is given by v = 〈 x − y , z + y + 4 , z 2 〉

Solution Summary: The author calculates the flow rate of water across the net given by y = 1 x 2 z 2 and the velocity vector field for the river.

Videos

To calculate: The flow rate of water across the net given by y=1−x2−z2,y≥0 oriented in the positive y-direction if the velocity vector field for the river is given by v=〈x−y,z+y+4,z2〉

Want to see the full answer?

Chapter 17 Solutions

To calculate: The flow rate of water across the net given by $y = \sqrt{1 - x^{2} - z^{2}}, y \geq 0$ oriented in the positive y-direction if the velocity vector field for the river is given by $v = 〈 x - y, z + y + 4, z^{2} 〉$