Solution Carbon dioxide flows through a nozzle. The inlet temperature and velocity and the exit temperature of CO2 are specified.
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The Mach number is to be determined at the inlet and exit of the nozzle. Assumptions 1 CO2 is an ideal gas with constant specific heats at room temperature. T Solution Nitrogen flows through a heat exchanger. The inlet temperature, pressure, and velocity and the exit pressure and velocity are specified.
The Mach number is to be determined at the inlet and exit of the heat exchanger. Assumptions 1 N2 is an ideal gas. Solution The speed of sound in refrigeranta at a specified state is to be determined. Assumptions Ra is an ideal gas with constant specific heats at room temperature. Assumptions Air is an ideal gas with constant specific heats at room temperature. The Mach number of a rocket, for example, will be increasing even when it ascends at constant speed. Also, the specific heat ratio k changes with temperature.
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The Mach number of steam is to be determined assuming ideal gas behavior. Assumptions Steam is an ideal gas with constant specific heats. Therefore, the ideal gas approximation is a reasonable one in this case. The ratio of the initial to the final speed of sound is to be determined. The specific heat ratio k varies with temperature, but in our case this change is very small and can be disregarded. Assumptions Helium is an ideal gas with constant specific heats at room temperature.
Viscosity C Solution We are to discuss Newtonian fluids. Analysis Fluids whose shear stress is linearly proportional to the velocity gradient shear strain are called Newtonian fluids. Most common fluids such as water, air, gasoline, and oils are Newtonian fluids. Discussion In the differential analysis of fluid flow, only Newtonian fluids are considered in this textbook. It is due to the internal frictional force that develops between different layers of fluids as they are forced to move relative to each other.
Viscosity is caused by the cohesive forces between the molecules in liquids, and by the molecular collisions in gases.
Fluid Mechanics: Fundamentals and Applications
In general, liquids have higher dynamic viscosities than gases. Analysis a For liquids, the kinematic viscosity decreases with temperature. Discussion You can easily verify this by looking at the appendices. Analysis When two identical small glass balls are dropped into two identical containers, one filled with water and the other with oil, the ball dropped in water will reach the bottom of the container first because of the much lower viscosity of water relative to oil. Discussion Oil is very viscous, with typical values of viscosity approximately times greater than that of water at room temperature.
The viscosity of the fluid is to be determined. Viscosity is a strong function of temperature, and the values can be significantly different at different temperatures. The constants of Sutherland correlation for carbon dioxide are to be determined and the viscosity of carbon dioxide at a specified temperature is to be predicted and compared to the value in table A Analysis Sutherland correlation is given by Eq.
The friction drag force exerted on the pipe by the fluid in the flow direction per unit length of the pipe is to be determined. Assumptions The viscosity of the fluid is constant. Discussion Note that the drag force acting on the pipe in this case is independent of the pipe diameter. The location in oil where the velocity is zero and the force that needs to be applied on the plate are to be determined.
Assumptions 1 The thickness of the plate is negligible. Analysis a The velocity profile in each oil layer relative to the fixed wall is as shown in the figure below.
The point of zero velocity is indicated by point A, and its distance from the lower plate is determined from geometric considerations the similarity of the two triangles in the lower oil layer to be 2. We are also to explain what happens when the gap gets bigger. Assumptions 1 The fluid is incompressible and Newtonian.
The thickness of the gap is h, and we let y be the distance from the outer wall into the fluid towards the inner wall. Also, we are asked for the torque required to turn the inner cylinder. This applied torque is counterclockwise mathematically positive. As long as the gap is very small, and therefore the wall curvature effects are negligible, this approximation should be very good. Another way to think about this is that when the gap is very small compared to the cylinder radii, a magnified view of the flow in the gap appears similar to flow between two infinite walls Couette flow.
However, as the gap increases, the curvature effects are no longer negligible, and the linear velocity profile is not expected to be a valid approximation. We do not expect the velocity to remain linear as the gap increases. Discussion It is possible to solve for the exact velocity profile for this problem, and therefore the torque can be found analytically, but this has to wait until the differential analysis chapter.
Chapter 2 Properties of Fluids r r Solution A clutch system is used to transmit torque through an oil film between two identical disks. For specified rotational speeds, the transmitted torque is to be determined. Assumptions 1 The thickness of the oil film is uniform. Limited distribution permitted only to teachers and educators for course preparation.
If you are a student using this Manual, you are using it without permission. Analysis The previous problem is reconsidered. Using EES software, the effect of oil film thickness on the torque transmitted is investigated. Film thickness varied from 0. The EES Equations window is printed below, followed by the 32h tabulated and plotted results.
The force that needs to be applied in the horizontal direction when the block is dry, and the percent reduction in the required force when an oil film is applied on the surface are to be determined. Assumptions 1 The inclined surface is plane perfectly flat, although tilted. Analysis a The velocity of the block is constant, and thus its acceleration and the net force acting on it are zero. A free body diagram of the block is given.
Then the shear force is expressed as V shear w s s 50 cm 0.
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A relation for the wall shear stress is to be obtained. Assumptions The fluid is Newtonian. A relation for friction drag force exerted on the pipe and its numerical value for water are to be determined. Assumptions 1 The flow through the circular pipe is one-dimensional. The power required to maintain this motion and the reduction in the required power input when the oil temperature rises are to be determined.
Assumptions The thickness of the oil layer remains constant. Discussion Note that the power required to overcome shear forces in a viscous fluid greatly depends on temperature. The thickness of the gap is h, and we let y be the distance from the outer wall into the fluid towards the inner wall as sketched.