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For Later 47 47 found this document useful, Mark this document as useful 53 53 found this document not useful, Mark this document as not useful Embed Share Print Download Now Jump to Page You are on page 1 of 116 Search inside document Browse Books Site Directory Site Language: English Change Language English Change Language. Share with your friends to get theI submitted this earlier and there must be different versions. In my book,problem 117 has a pressurized tank. The top layer contains air at 75 kPa and below that is 85 cm water. It flows out of the bottom turning up creating a jet and askshow high the water jet rises. Steady frictionless flow. It gives me confidence when I can compare my answer.A constant pressure gradient in a direction parallel to the plates is suddenly appliedand the fluid starts to move. Determine the appropriate differential equation(s), initial condition, and boundary equations that govern this type of flow. You need notsolve the equation(s).Thank you! 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Analysis (a) From the definition, we have Integrating With the given data we obtain (b) Eq. 2?13 can be rearranged to give or which is identical with (a). Chapter 2 Properties of Fluids 2-125 Solution The velocity profile for laminar one-dimensional flow between two parallel plates is given. A relation for friction drag force exerted on the plates per unit area of the plates is to be obtained. ? u ( y ) ? 4u max y h ? ? y h ?2 Assumptions 1 The flow between the plates is one-dimensional. 2 The fluid is Newtonian. Analysis ? The velocity profile is given by u ( y ) ? 4u max y h ? ? y h ?2 ? where h is the distance between the two plates, y is the vertical distance from the bottom plate, and umax is the maximum flow velocity that occurs at midplane. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part. ? Chapter 2 Properties of Fluids 2-126 Solution Two immiscible Newtonian liquids flow steadily between two large parallel plates under the influence of an applied pressure gradient. The lower plate is fixed while the upper one is pulled with a constant velocity. The velocity profiles for each flow are given. The values of constants are to be determined. An expression for the viscosity ratio is to be developed. The forces and their directions exerted by liquids on both plates are to be determined. Assumptions 1 The flow between the plates is one-dimensional. 2 The fluids are Newtonian. Properties The viscosity of fluid one is given to be. Chapter 2 Properties of Fluids 2-127 Solution A shaft is pulled with a constant velocity through a bearing. The space between the shaft and bearing is filled with a fluid. The force required to maintain the axial movement of the shaft is to be determined. Assumptions 1 The fluid is Newtonian. Properties The viscosity of the fluid is given to be 0.1 Pa?s. Analysis Bearing Viscous oil, Shaft The varying clearance obtain can be expressed as a function of axial coordinate (see figure). Chapter 2 Properties of Fluids 2-128 Solution A shaft rotates with a constant angual speed in a bearing. The torque required to maintain the motion is to be determined. Properties The viscosity of the fluid is given to be 0.1 Pa?s. Analysis The varying clearance can be expressed as a function of axial coordinate (see figure below). According to this sketch we obtain Assuming a linear velocity distribution in the gap, the viscous force acting on the differential strip element is where in this case. Chapter 2 Properties of Fluids 2-129 Solution A cylindrical shaft rotates inside an oil bearing at a specified speed. The power required to overcome friction is to be determined. Assumptions 1 The gap is uniform, and is completely filled with oil. 2 The end effects on the sides of the bearing are negligible. 3 The fluid is Newtonian. The height that water can rise in those tubes is to be determined. Therefore, the value determined may change with temperature. The pressure of the gas is (a) 7 kPa (b) 72 kPa (c) 105 kPa (d) 460 kPa (e) 4630 kPa Answer (c) 105 kPa Solution Solved by EES Software. Solutions can be verified by copying-and-pasting the following lines on a blank EES screen. (Similar problems and their solutions can be obtained easily by modifying numerical values). The partial pressure of water vapor in this gas mixture is (a) 5 kPa (b) 9.1 kPa (c) 10 kPa (d) 22.7 kPa (e) 100 kPa Answer (b) 9.1 kPa Solution Solved by EES Software. If the temperature of water in the pipe is 180?C, the vapor pressure of water in the pipe is (a) 1002 kPa (b) 180 kPa (c) 101.3 kPa (d) 18 kPa (e) 100 kPa Answer (a) 1002 kPa Solution Solved by EES Software. Chapter 2 Properties of Fluids 2-136 In a water distribution system, the pressure of water can be as low as 1.4 psia. The maximum temperature of water allowed in the piping to avoid cavitation is (a) 50?