Recap: Equations of Motion & Mechanical Energy | Fluid Mechanics for Civil Engineering - Civil Engineering (CE) PDF Download

Recap
In this course you have learnt the following
 

• The total mechanical energy of a fluid element in an inviscid and irrotational flow remains the same everywhere in the flow field, while it does so only along a streamline in an inviscid but rotational flow. 
   
• Flows having only tangential velocities with streamlines as concentric circles are known as plane circular vortex flows. A free vortex flow is an irrotational vortex flow where the total mechanical energy of the fluid elements remains same in the entire flow field and the tangential velocity is inversely proportional to the radius of curvature. A forced vortex flow is a rotational vortex flow where the tangential velocity is directly proportional to the radius of curvature. Pressure in vortex flows increases with an increase in the radius of curvature. Spiral vortex flows are obtained as a result of superimposition of a plane circular vortex flow with a purely radial flow.
   
• Apart from losses due to friction, the loss of mechanical energy is incurred, in course of flow through a closed duct, when the path of the fluid stream is suddenly changed due to any abrupt change in the geometry of the duct. In long ducts, these losses are very small as compared to the friction loss and hence they are termed as minor losses. These include (i) losses due to an abrupt enlargement of the cross-section of a duct, (ii) losses due to an abrupt contraction of the cross-section of a duct, (iii) losses due to the exist from a small pipe or duct to a large reservoir, and (iv) losses due to the entrance from a large reservoir to a small pipe or duct. 
   
• Venturimeter, Orificemeter and Flow nozzle are the typical flow meters which measure the rate of flow of a fluid through a pipe by providing a coaxial area contraction within the pipe and thus creating a pressure drop across the contraction. The flow rate is measured by determining the velocity of flow at the constricted section in terms of the pressure drop by the application of Bernoulli’s equation. 
   
• A venturimeter is a short pipe consisting of two conical parts with a sort uniform cross-section, in between, known as throat. 
   
• An orificementer is a thin circular plate with a sharp edged concentric circular hole in it. 
   
• A flow nozzle is a short conical tube providing only a convergent passage to the flow. In a comparison between the three flow meters, a venturimeter is the most accurate but the most expensive, while the orificemeter is the least expensive but the least accurate. Flow nozzle falls in between these two.
   
• The static pressure in a fluid is the thermodynamic pressure defining the state of fluid and becomes equal to the arithmetic average of the normal stresses at a point in case of a real and Stoksian fluid. The stagnation pressure at a point in a fluid flow is the pressure which could result if the fluid were brought to rest isentropically. The difference between the stagnation and static, pressure is the pressure equivalence of the velocity head ( 1/ 2ρV ²) and is known as dynamic pressure. 
   
• An instrument which contains tubes to record the stagnation and static pressures in a flow to finally determine the flow velocity and flow rate is known as a Pitot static tube.
   
• An orifice is a small aperture through which the fluid passes. The liquid from a tank is usually discharged through a small orifice at its side. A drowned or submerged orifice is one which does not discharge into open atmosphere, but discharge into liquid of the same kind. The discharge through an orifice is increased by fitting a short length of pipe to the outside known as external mouthpiece. The discharge rate is increased due to a decrease in the pressure at vena contracta within the mouthpiece resulting in an increase in the effective head causing the flow.