Stagnation point pressure

This states that the sum of the velocity pressure 0.5pv plus the static pressure / the total pressure, is constant along a streamline. In the case of standard air density (1.2 kg m ), 0.5pv becomes 0.6v. When a Pitot-static tube is immersed into the flow, as in Fig. 12.19, the velocity at the stagnation point at the tube nose is f = 0 and the local static pressure equals the total pressure p,. The flow static pressure p, is measured a short distance downstream from the surface of the tube. The flow velocity is obtained by applying Eq. (12.27) ... 

The pitot tube is a device for measuring v(r), the local velocity at a given position in the conduit, as illustrated in Fig. 10-1. The measured velocity is then used in Eq. (10-2) to determine the flow rate. It consists of a differential pressure measuring device (e.g., a manometer, transducer, or DP cell) that measures the pressure difference between two tubes. One tube is attached to a hollow probe that can be positioned at any radial location in the conduit, and the other is attached to the wall of the conduit in the same axial plane as the end of the probe. The local velocity of the streamline that impinges on the end of the probe is v(r). The fluid element that impacts the open end of the probe must come to rest at that point, because there is no flow through the probe or the DP cell this is known as the stagnation point. The Bernoulli equation can be applied to the fluid streamline that impacts the probe tip ... 

At all values of the particle Reynolds number Rep, the fluid is brought to rest relative to the particle at A, which is therefore a stagnation point where the pressure is higher than in the flowing fluid (see equation 1.19 in... 

Interestingly, the shape of the wake is similar to that developed behind a hypersonic blunt body where the flow converges to form a narrow recompression neck region several body diameters downstream of the rear stagnation point due to strong lateral pressure gradients. The liquid material, that is continuously stripped off from the droplet surface, is accelerated almost instantaneously to the particle velocity behind the wave front and follows the streamline pattern of the wake, suggesting that the droplet is reduced to a fine micromist. 

In the opposed jets design fluid is sucked or pumped into a beaker. The profile which develops is dominantly extensional. In the profiled slot design a rectangular channel is designed such that in the total slip condition an extensional flow develops with a constant rate. The pressure is measured at the stagnation point. Other designs include the open syphon, where fluid is sucked from a beaker through a nozzle which is... 

At the stagnation point at the nose of the slug, the pressure is Pi (also the pressure inside the bubble) applying Bernoulli s equation between sections 0 and 1, we obtain... 

Previous workers have also made use of potential flow pressure distributions about spheroids, but no allowance was made for lack of fore-and-aft symmetry, while the constant pressure condition was satisfied only near the front stagnation point (SI) or at the equator and poles (H6, Mil). 

Note also Ihe variation of Ihe profile near the surface of the plate. Skin friction has steadily decelerated the individual fluid particles, lire profile at n indicates that Ihe lower portion has come to rest. This is known as the stagnation point. Air-llow phenomena in this region arc important in many ways, especially when there is an intended rising downstream pressure gradient, as in diflfuser lubes or over the surface of airfoils. 

Vertical reactor or stagnation point flow reactor at atmospheric and reduced pressure conditions... 

Stagnation pressure. The center streamline shows that the velocity becomes zero at the stagnation point. If p0/w denotes the static pressure head at some distance away where the velocity is Va, while pjw denotes the pressure head at the stagnation point, then, applying Eq. (10.8) to these two points, p0/w + 0 + V2l2g = pjw + 0 + 0, or the stagnation pressure is ... 

The flow profiles with H > 2.591, correspond to velocity distributions with inflection point and these are the decelerated flows or flows with adverse pressure gradient. On the contrary, the flow profiles with H < 2.591, correspond to - < 0 (the accelerated flows). The figure with = 0 and H = 2.59, corresponds to the Blasius profile. The profile with j3h = I and H = 2.22 corresponds to the stagnation point flow. The other two profiles in Fig. 2.7 are for flows with adverse pressure gradient and the crosses on the profile indicate the locations of the inflexion point. The profile for /3h = —0.1988 H = 4.032) corresponds to the case of incipient separation. 

The presence of adverse pressure gradients induces separation towards the rear stagnation point (Figure Ic). Whereas its influence on the gas-phase motion may not be critical, its effect on the liquid-phase motion may be quite significant because of the closed streamlines. If this is the case, then entirely different formulations may be required to account for the effects from separation and the wake. Such a detailed analysis has not been performed for either the gas or the liquid flow. 

Fig. 18. CO coverage (H) as a function of the Pt substrate temperature measured during CO oxidation at a pressure of 20 mbar. (D) indicate temperatures where equilibrium CO surface coverage was too low to be detected. CO2 production (A) simultaneously measured by mass spectrometry in the exhaust gas. The measurement were carried out under laminar flow conditions in a stagnation point flow onto the Pt catalyst surface. Solid lines are results of a numerical reactive flow simulation for a CO/02/Ar-stagnation point flow onto the Pt foil corresponding to the experimental flow conditions (CO 15 seem O2 30 seem Ar 105 seem).

Cross-flow over a cylinder exhibits complex flow patterns, as shown in Fig. 7-16, The fluid approaching the cylinder branches out and encircles the cylinder, forming a boundary layer that wraps around the cylinder. The fluid particles on Ihe inidplane strike Ihe cylinder at Ihe stagnation point, bringing the fluid to a complete stop and ihus raising the pressure at that point. The pressure decreases in the flow direction while the fluid velocity increases. 

The Bernoulli theorem may be used to determine the change in pressure caused by retardation of fluid at the upstream side of a body immersed in a fluid stream. This principle is applied in the Pitot tube, shown in Fig. 1C. The fluid velocity is reduced from Ma. the velocity of the fluid filament in alignment with the tube, to zero at B, an position known as the stagnation point. The pressure, P, is measured at this point by the method shown in Fig.l C. The undisturbed pressure, P, is measured in this example with a tapping point in the wall connected to a manometer. 

Krahn [76] explained how the rotation of the sphere would cause the transition from laminar to turbulent boundary layers at different rotational velocities at the two sides of a sphere. The direction of the asymmetrical wake was explained based on the separation points for laminar and turbulent boundary layers. Krahn studied the flow around a cylinder. For a non-rotating cylinder the laminar boundary layer separates at 82° from the forward stagnation point, while the turbulent boundary layer separates at about 130°. Due to the rotation the laminar separation point will move further back, while the turbulent separation point will move forward. For some value of v qaa/v between 0 and 1 the laminar and turbulent separation points will be at equal distance from the stagnation point. The pressure on the turbulent side will be smaller than on the laminar side causing a negative Magnus force. 

Figure 10-9. The dimensionless shear stress as a function of position on the surface of a circular cylinder as calculated with the approximate Blasius series solution. Note that x is measured in radians from the front-stagnation point. The predicted point of boundary-layer separation corresponds to the second zero of du/dY 0. and is predicted to occur just beyond the minimum pressure point atx = jt/2.

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