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37-401: P25 may refer to: Boulton & Paul P.25 Bugle , a British heavy bomber BRM P25 , a Formula One racing car Honda P25 , a moped Mabiha language P-25 mine , an Italian anti-personnel mine Papyrus 25 , a biblical manuscript Phosphorus-25 , an isotope of phosphorus Project 25 , a telecommunication standard Project 2025 ,

74-410: A US political plan Zastava P25 , a pistol a medium-format camera back by Phase One See also [ edit ] 25P (disambiguation) [REDACTED] Topics referred to by the same term This disambiguation page lists articles associated with the same title formed as a letter–number combination. If an internal link led you here, you may wish to change the link to point directly to

111-484: A certain moment in time, and observed at a later instant. Streamlines are defined by d x → S d s × u → ( x → S ) = 0 → , {\displaystyle {d{\vec {x}}_{S} \over ds}\times {\vec {u}}({\vec {x}}_{S})={\vec {0}},} where " × {\displaystyle \times } " denotes

148-462: A flow do not intersect, because a fluid particle cannot have two different velocities at the same point. However, pathlines are allowed to intersect themselves or other pathlines (except the starting and end points of the different pathlines, which need to be distinct). Streaklines can also intersect themselves and other streaklines. Streamlines and timelines provide a snapshot of some flowfield characteristics, whereas streaklines and pathlines depend on

185-517: A greater degree of streamlining and a slightly elevated all-up weight. Despite the type having demonstrated exceptional maneuverability and good performance in general, aviation historian Alec Brew observed that constrained budgets had prevented a production order from being placed for the Bugle. Instead, the Air Ministry pursued a policy of continuing to order increasingly advanced prototypes across

222-533: A new twin-engined heavy bomber to equip the Royal Air Force (RAF). However, this effort was not a clean-sheet design, as it drew extensively on the company's existing experiences with aircraft such as the Boulton Paul Bolton and Boulton & Paul Bourges . The new design actually shared its basic configuration with the preceding Bourges, which had been developed during the final months of

259-411: A range of manufacturers as to foster innovation and advancement in industry, as well as readiness to put such designs into quantity production should a military need arise. Data from Boulton Paul Aircraft since 1915 , The British Bomber since 1912 General characteristics Performance Armament Streamlined By definition, different streamlines at the same instant in

296-459: A single gun turret , to the rear of which the fuselage tapered inwards in a triangular fashion as to maximise the gunner's downwards field of fire. The position of the gunners were deliberately lower than that of the pilot's cockpit, giving the latter a favourable level of visibility. The aircraft's nose gunner also acted as the bomb-aimer, and was provided with separate rudder controls to the pilot to make minor adjustments during bombing runs; all of

333-466: Is a time of interest. In steady flow (when the velocity vector-field does not change with time), the streamlines, pathlines, and streaklines coincide. This is because when a particle on a streamline reaches a point, a 0 {\displaystyle a_{0}} , further on that streamline the equations governing the flow will send it in a certain direction x → {\displaystyle {\vec {x}}} . As

370-414: Is inside a stream surface must remain forever within that same stream surface, because the streamlines are tangent to the flow velocity. A scalar function whose contour lines define the streamlines is known as the stream function . Dye line may refer either to a streakline: dye released gradually from a fixed location during time; or it may refer to a timeline: a line of dye applied instantaneously at

407-450: Is steady, so that they can use experimental methods of creating streaklines to identify the streamlines. Knowledge of the streamlines can be useful in fluid dynamics. The curvature of a streamline is related to the pressure gradient acting perpendicular to the streamline. The center of curvature of the streamline lies in the direction of decreasing radial pressure. The magnitude of the radial pressure gradient can be calculated directly from

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444-451: Is the pressure gradient and ∂ c ∂ s {\displaystyle {\frac {\partial c}{\partial s}}} the velocity gradient along the streamline. For a steady flow, the time derivative of the velocity is zero: ∂ c ∂ t = 0 {\displaystyle {\frac {\partial c}{\partial t}}=0} . g {\displaystyle g} denotes

481-699: Is the velocity of a particle P {\displaystyle P} at location x → {\displaystyle {\vec {x}}} and time t {\displaystyle t} . The parameter τ P {\displaystyle \tau _{P}} , parametrizes the streakline x → s t r ( t , τ P ) {\displaystyle {\vec {x}}_{str}(t,\tau _{P})} and t 0 ≤ τ P ≤ t {\displaystyle t_{0}\leq \tau _{P}\leq t} , where t {\displaystyle t}

518-475: The First World War with positive results, but had been terminated prior to procurement as a part of the rapidly implemented military cutbacks made after the conflict's end. The Air Ministry was suitably interested in the proposal that a pair of prototypes, J6984 and J6985 , were ordered for evaluation purposes. In response to an Air Ministry directive which forbid the placement of fuel tanks within

555-425: The vector cross product and x → S ( s ) {\displaystyle {\vec {x}}_{S}(s)} is the parametric representation of just one streamline at one moment in time. If the components of the velocity are written u → = ( u , v , w ) , {\displaystyle {\vec {u}}=(u,v,w),} and those of

592-464: The bombs were stored externally on four bomb rails, two attached to the lower longerons and two fitted underneath the lower wings. The undercarriage and tailskid both were furnished with oleo - pneumatic shock absorbers, while main wheels akin to that of the Bourges were fitted. Additional dampening was provided via a pair of tubes fitted with coil springs attached to the main landing gear. During

629-468: The competing Vickers Virginia , during which the former exhibited its considerably greater manoeuvrability and higher top speed in comparison to the latter. It was during 1925 that the first of the improved Bugle II s appeared, which was powered by a pair of Napier Lion engines, each capable of 450 hp, in place of the Jupiter engines. It also featured numerous refinements to the design, including

666-411: The curvature of the front surface can be much steeper than the back of the object. Most drag is caused by eddies in the fluid behind the moving object, and the objective should be to allow the fluid to slow down after passing around the object, and regain pressure, without forming eddies. The same terms have since become common vernacular to describe any process that smooths an operation. For instance, it

703-406: The curves are parallel to the velocity vector. Here s {\displaystyle s} is a variable which parametrizes the curve s ↦ x → S ( s ) . {\displaystyle s\mapsto {\vec {x}}_{S}(s).} Streamlines are calculated instantaneously, meaning that at one instance of time they are calculated throughout

740-414: The density of the fluid, the curvature of the streamline and the local velocity. Dye can be used in water, or smoke in air, in order to see streaklines, from which pathlines can be calculated. Streaklines are identical to streamlines for steady flow. Further, dye can be used to create timelines. The patterns guide design modifications, aiming to reduce the drag. This task is known as streamlining , and

777-532: The direction s {\displaystyle s} of the streamline is denoted by c {\displaystyle c} . r {\displaystyle r} is the radius of curvature of the streamline. The density of the fluid is denoted by ρ {\displaystyle \rho } and the kinematic viscosity by ν {\displaystyle \nu } . ∂ p ∂ s {\displaystyle {\frac {\partial p}{\partial s}}}

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814-425: The equations that govern the flow remain the same when another particle reaches a 0 {\displaystyle a_{0}} it will also go in the direction x → {\displaystyle {\vec {x}}} . If the flow is not steady then when the next particle reaches position a 0 {\displaystyle a_{0}} the flow would have changed and

851-862: The fluid from the instantaneous flow velocity field . A streamtube consists of a bundle of streamlines, much like communication cable. The equation of motion of a fluid on a streamline for a flow in a vertical plane is: ∂ c ∂ t + c ∂ c ∂ s = ν ∂ 2 c ∂ r 2 − 1 ρ ∂ p ∂ s − g ∂ z ∂ s {\displaystyle {\frac {\partial c}{\partial t}}+c{\frac {\partial c}{\partial s}}=\nu {\frac {\partial ^{2}c}{\partial r^{2}}}-{\frac {1}{\rho }}{\frac {\partial p}{\partial s}}-g{\frac {\partial z}{\partial s}}} The flow velocity in

888-424: The full time-history of the flow. However, often sequences of timelines (and streaklines) at different instants—being presented either in a single image or with a video stream—may be used to provide insight in the flow and its history. If a line, curve or closed curve is used as start point for a continuous set of streamlines, the result is a stream surface . In the case of a closed curve in a steady flow, fluid that

925-425: The fuselage, fuel was instead accommodated within semi-circular tanks hung beneath the upper wing's inner bay area. The engines, which were initially a pair of Bristol Jupiter II air-cooled radial engines , each capable of producing up to 400 hp (298 kW), were housed within streamlined nacelles that had a patented hinged mounting, which was designed so that the engines could be swung out of situ while on

962-712: The gravitational acceleration. Pathlines are defined by { d x → P d t ( t ) = u → P ( x → P ( t ) , t ) x → P ( t 0 ) = x → P 0 {\displaystyle {\begin{cases}{\dfrac {d{\vec {x}}_{P}}{dt}}(t)={\vec {u}}_{P}({\vec {x}}_{P}(t),t)\\[1.2ex]{\vec {x}}_{P}(t_{0})={\vec {x}}_{P0}\end{cases}}} The subscript P {\displaystyle P} indicates that we are following

999-442: The ground for ease of maintenance. The structural elements of the Bugle were primarily composed of steel , with some portions being corrugated for additional strength, while the exterior had a fabric covering. The interplane strut design, which was a patented feature at that time, used a combination of steel inner struts and duralumin outer ones, while the removable fairings were made of wood. This use of light alloys in some of

1036-398: The intended article. Retrieved from " https://en.wikipedia.org/w/index.php?title=P25&oldid=1237608435 " Category : Letter–number combination disambiguation pages Hidden categories: Short description is different from Wikidata All article disambiguation pages All disambiguation pages Boulton %26 Paul P.25 Bugle The Boulton & Paul Bugle

1073-1299: The motion of a fluid particle. Note that at point x → P {\displaystyle {\vec {x}}_{P}} the curve is parallel to the flow velocity vector u → {\displaystyle {\vec {u}}} , where the velocity vector is evaluated at the position of the particle x → P {\displaystyle {\vec {x}}_{P}} at that time t {\displaystyle t} . Streaklines can be expressed as, { d x → s t r d t = u → P ( x → s t r , t ) x → s t r ( t = τ P ) = x → P 0 {\displaystyle {\begin{cases}\displaystyle {\frac {d{\vec {x}}_{str}}{dt}}={\vec {u}}_{P}({\vec {x}}_{str},t)\\[1.2ex]{\vec {x}}_{str}(t=\tau _{P})={\vec {x}}_{P0}\end{cases}}} where, u → P ( x → , t ) {\displaystyle {\vec {u}}_{P}({\vec {x}},t)}

1110-423: The particle will go in a different direction. This is useful, because it is usually very difficult to look at streamlines in an experiment. However, if the flow is steady, one can use streaklines to describe the streamline pattern. Streamlines are frame-dependent. That is, the streamlines observed in one inertial reference frame are different from those observed in another inertial reference frame. For instance,

1147-453: The resulting design is referred to as being streamlined . Streamlined objects and organisms, like airfoils , streamliners , cars and dolphins are often aesthetically pleasing to the eye. The Streamline Moderne style, a 1930s and 1940s offshoot of Art Deco , brought flowing lines to architecture and design of the era. The canonical example of a streamlined shape is a chicken egg with the blunt end facing forwards. This shows clearly that

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1184-400: The secondary structural members represented a loosening of formerly negative attitudes on the part of the Air Ministry towards the use of such materials. The fuselage was rectangular in shape, its frame formed from four longerons and built in two sections. Struts and bracing wires alike attached to an angle plane, which was attached to the fuselage via bearings. The dorsal fuselage featured

1221-472: The streamline as x → S = ( x S , y S , z S ) , {\displaystyle {\vec {x}}_{S}=(x_{S},y_{S},z_{S}),} we deduce d x S u = d y S v = d z S w , {\displaystyle {dx_{S} \over u}={dy_{S} \over v}={dz_{S} \over w},} which shows that

1258-401: The streamlines in the air around an aircraft wing are defined differently for the passengers in the aircraft than for an observer on the ground. In the aircraft example, the observer on the ground will observe unsteady flow, and the observers in the aircraft will observe steady flow, with constant streamlines. When possible, fluid dynamicists try to find a reference frame in which the flow

1295-432: The type's maiden flight , piloted by Frank Courtney. The second prototype conducted its own maiden flight later that same year. During 1924, a third aircraft equipped with more powerful Bristol Jupiter IV engines, appeared; other changes on this aircraft included a four-seat configuration, a slightly reduced wingspan, and increased fuel capacity. In 1925, service trials commenced with the third aircraft, facing off against

1332-399: The type's taxiing trials, the aircraft proved to be more stable than its immediate preceding designs. The rudder was equipped with a locking device as to better handle asymmetric flight conditions, such as single-engine operations. Unlike the company's earlier designs, the aircraft's four ailerons were actuated via struts rather than cables. On 30 June 1923, the first prototype performed

1369-627: Was a heavy bomber designed and produced by the British manufacturing group Boulton & Paul . There were two variants; the Bugle I with 400 hp (298 kW) Bristol Jupiter II radial engines (five built) and the Napier Lion W-block Bugle II (two built) Work on what would become the Bugle effectively commenced at Boulton & Paul following the Air Ministry 's release of Specification 30/22 , which sought

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