Calculus
7th Edition
ISBN: 9781524916817
Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE
Publisher: Kendall Hunt Publishing
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Chapter 13.5, Problem 55PS
To determine
To calculate: The outward rate of fluid flow through the paraboloid
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. Seawater has a density 1025 kg/m3 and flows in a velocity field v = yi + xj where x, y, and z are
measured in meters and the components of v meters per second. Find the rate of flow outward through
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A fluid has density 2 kg/m³ and flows in a velocity field v = -yi+xj+2z k where x, y, and z are
measured in meters and the components of v in meters per second.
Find the rate of flow outward through the sphere x² + y² + z² = 4
A fluid has density 600 kg/m³ and flows with velocity v = x + yj + zk, where x, y, and z are
measured in meters, and the components of are measured in meters per second. Find the rate of
flow outward through the part of the paraboloid z = 4 - x² - y² that lies above the xy plane.
kg/s
Chapter 13 Solutions
Calculus
Ch. 13.1 - Prob. 1PSCh. 13.1 - Prob. 2PSCh. 13.1 - Prob. 3PSCh. 13.1 - Prob. 4PSCh. 13.1 - Prob. 5PSCh. 13.1 - Prob. 6PSCh. 13.1 - Prob. 7PSCh. 13.1 - Prob. 8PSCh. 13.1 - Prob. 9PSCh. 13.1 - Prob. 10PS
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Prob. 60CRP
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- Seawater has density 1025 kg/m³ and flows in a velocity field v = yi + x j, where x, y, and z are measured in meters and the components of v in meters per second. Find the rate of flow outward through the hemisphere x² + y² + z² = 36, z ≥ 0. kg/sarrow_forwardA fluid has density 600 kg/m³ and flows with velocity v = xi +yj + zk, where x, y, and z are measured in meters, and the components of 7 are measured in meters per second. Find the rate of flow outward through the part of the paraboloid z = 25 – x² - y² that lies above the xy plane. kg/sarrow_forwardConsider the unsteady flow u = uo, v = kt, w = 0 where uo and k are positive constants. Show that the streamlines are straight lines, and sketch them at two different times. Also show that any fluid particle flows a parabolic path as time proceeds.arrow_forward
- Seawater has density 1025 kg/m and flows in a velocity field v = yi + xj, where x, y, and z are measured in meters and the components of v in meters per second. Find the rate of flow outward through the hemisphere x² + y² + z² = 9, z > 0.arrow_forwardA fluid has density 1200 kg/m³ and flows with velocity ī = measured in meters, and the components of ī are xi + yj + zk, where x, y, and z are measured in meters per second. Find the rate of flow outward through the part of the paraboloid z = 49 – x² – y? that lies above the xy plane. - kg/sarrow_forwardA fluid has density 1000 kg/m³ and flows with velocity v = xi + yj + zk, where position is measured in meters, and speed is measured in meters per second. Find the rate of flow outward through the part of the paraboloid æ = 36 – y² – 22 where a > 0. kg/sarrow_forward
- Seawater has density 1025 kg/m³ and flows in a velocity field v = yi + x j, where x, y, and z are measured in meters and the components of v in meters per second. Find the rate of flow outward through the hemisphere x2 + y2 + z2 = 64, z 2 0. kg/sarrow_forwardA fluid has density 900 kg/m³ and flows with velocity v = zi+yj + zk, where x, y, and z are measured in meters, and the components of are measured in meters per second. Find the rate of flow outward through the part of the paraboloid z = 1-2²2 - y² that lies above the xy plane. kg/sarrow_forwardA fluid has density 1000 kg/m3 and flows with velocity ū = xi + yj + zk, where x, y, and z are measured in meters, and the components of ū are measured in meters per second. Find the rate of flow outward through the part of the paraboloid z = 4 – x² – y that lies above the xy plane. kg/sarrow_forward
- A fluid has density 600 kg/m3 and flows with velocity i = xi + yj + zk, where x, y, and z are measured in meters, and the components of ū are measured in meters per second. Find the rate of flow outward through the part of the paraboloid z = 36 – a² – y² that lies above the xy plane. kg/sarrow_forwardLet v = zk be the velocity field (in meters per second) of a fluid in R3. Calculate the flow rate (in cubic meters per second) through the upper hemisphere (z > 0) of the sphere x 2 + y2 + z2 = 1.arrow_forwardA fluid has density 1000 kg/m³ and flows with velocity i = xi + yj + zk, where x, y, and z are measured in meters, and the components of v are measured in meters per second. Find the rate of flow outward through the part of the paraboloid z = 49 – x? – y² that lies above the xy plane. kg/sarrow_forward
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