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This can be done as follows,. Example 5: A person challenged himself to cross a small river and back. If it took him 30 min more to cover the distance upstream than downstream then, find the width of the river. If a boat takes t hours to row to a place and return back, then the distance between the two places can be estimated through. If in a river running at 1. Sol To solve this question we will simply use the formula given above. In this case, t is 50 minutes b is 1.
The above examples are just few simple and basic application of the methods stated along with them. These formulas can come in handy and can save lot of your time in exam.
You can find questions and problems involving simultaneous use of more than one formula at times. But if you know the correct utilization of them you can solve any problem easily.
And, this smoothness comes with practice so the more you varied questions you try the more you will learn and become better at solving them. So, keep practicing! Enroll Now Rs. Your email address will not be published. How far is the place? If the speed of the stream be 3 kmph, what is the speed of the boat in still water? Let the speed of the boat in still water be x kmph. A motorboat went the river for 14 km and then up the river for 9 km.
It took a total of 5 hrs the entire journey. A person can row with the stream at 8 km per hour and against the stream at 6 km an hour. The speed of the current is. In a stream running at 2 Kmph, a motor boat goes 10 Km upstream and back again to the starting point in 55 minutes. Find the speed of motor boat in still water? A man can row 24 kmph in still water.
It takes him thrice as long to row up as to row down the river. Find the rate of the stream? The man's speed against the current is:. A lock is a device used for raising and lowering boats , ships and other watercraft between stretches of water of different levels on river and canal waterways. The distinguishing feature of a lock is a fixed chamber in which the water level can be varied; whereas in a caisson lock , a boat lift , or on a canal inclined plane , it is the chamber itself usually then called a caisson that rises and falls.
Locks are used to make a river more easily navigable, or to allow a canal to cross land that is not level. Later canals used more and larger locks to allow a more direct route to be taken. A pound lock is a type of lock that is used almost exclusively nowadays on canals and rivers. A pound lock has a chamber with gates at both ends that control the level of water in the pound.
In contrast, an earlier design with a single gate was known as a flash lock. Pound locks were first used in China during the Song Dynasty � AD , having been pioneered by the Song politician and naval engineer Qiao Weiyue in The distance between the two locks was rather more than 50 paces, and the whole space was covered with a great roof like a shed. The gates were 'hanging gates'; when they were closed the water accumulated like a tide until the required level was reached, and then when the time came it was allowed to flow out.
The water level could differ by 4 feet 1. In medieval Europe a sort of pound lock was built in at Vreeswijk , Netherlands. Yet the first true pound lock was built in at Damme near Bruges , Belgium.
When a stretch of river is made navigable, a lock is sometimes required to bypass an obstruction such as a rapid , dam , or mill weir � because of the change in river level across the obstacle.
In large scale river navigation improvements, weirs and locks are used together. A weir will increase the depth of a shallow stretch, and the required lock will either be built in a gap in the weir, or at the downstream end of an artificial cut which bypasses the weir and perhaps a shallow stretch of river below it.
A river improved by these means is often called a Waterway or River Navigation see example Calder and Hebble Navigation. Sometimes a river is made entirely non-tidal by constructing a sea lock directly into the estuary. Early completely artificial canals, across fairly flat countryside, would get round a small hill or depression by simply detouring contouring around it.
As engineers became more ambitious in the types of country they felt they could overcome, locks became essential to effect the necessary changes in water level without detours that would be completely uneconomic both in building costs and journey time. Later still, as construction techniques improved, engineers became more willing to cut directly through and across obstacles by constructing long tunnels , cuttings, aqueducts or embankments, or to construct even more technical devices such as inclined planes or boat lifts.
However, locks continued to be built to supplement these solutions, and are an essential part of even the most modern navigable waterways. The principle of operating a lock is simple. For instance, if a boat travelling downstream finds the lock already full of water:. If the lock were empty, the boat would have had to wait 5 to 10 minutes while the lock was filled. For a boat travelling upstream, the process is reversed; the boat enters the empty lock, and then the chamber is filled by opening a valve that allows water to enter the chamber from the upper level.
The whole operation will usually take between 10 and 20 minutes, depending on the size of the lock and whether the water in the lock was originally set at the boat's level. Boaters approaching a lock are usually pleased to meet another boat coming towards them, because Boat Travelling Upstream And Downstream Zero this boat will have just exited the lock on their level and therefore set the lock in their favour � saving about 5 to 10 minutes.
However, this is not true for staircase locks , where it is quicker for boats to go through in convoy. For simplicity, this section describes a basic type of lock, with a pair of gates at each end of the chamber and simple rack and pinion paddles raised manually by means of a detachable windlass operated by lock-keepers or the boat's shore crew.
This type can be found all over the world, but the terminology here is that used on the British canals. A subsequent section explains common variations. The rise is the change in water-level in the lock. The two deepest locks on the English canal system are Bath deep lock [6] [7] on the Kennet and Avon Canal and Tuel Lane Lock on the Rochdale Canal , which both have a rise of nearly 20 feet 6.
Both locks are amalgamations of two separate locks, which were combined when the canals were restored to accommodate changes in road crossings. By comparison, the Carrapatelo and Valeira locks on the Douro river in Portugal, which are feet 85 m long and 39 feet 12 m wide, have maximum lifts of feet 35 m and feet 33 m respectively. The upper chamber rises 60 feet 18 m and is connected to the lower chamber by a tunnel, which when descending does not become visible until the chamber is nearly empty.
A pound is the level stretch of water between two locks also known as a reach. The chamber is the main feature of a lock. It is a watertight masonry, brick, steel or concrete enclosure which can be sealed off from the pounds at both ends by means of gates.
The chamber may be the same size plus a little manoeuvring room as the largest vessel for which the waterway was designed; sometimes larger, to allow more than one such vessel at a time to use the lock. The chamber is said to be "full" when the water level is the same as in the upper pound; and "empty" when the level is the same as in the lower pound.
If the lock has no water in it at all, perhaps for maintenance work, it might also be said to be empty, but it is more usually described as "drained" or "de-watered". The cill , also spelled sill , is a narrow horizontal ledge protruding a short way into the chamber from below the upper gates. Allowing the rear of the boat to "hang" on the cill is the main danger when descending a lock, and the position of the forward edge of the cill is usually marked on the lock side by a white line.
The edge of the cill is usually curved, protruding less in the center than at the edges. In some locks, there is a piece of oak about 9 in 23 cm thick which protects the solid part of the lock cill.
On the Oxford Canal it is called a babbie; on the Grand Union Canal it is referred to as the cill bumper. Some canal operation authorities, primarily in the United States and Canada, call the ledge a miter sill mitre sill in Canada.
Water conservation gear on the Birmingham Canal Navigations. Gates are the watertight doors which seal off the chamber from the upper and lower pounds.
Each end of the chamber is equipped with a gate, or pair of half-gates, made of oak or elm or now sometimes steel.
The most common arrangement, usually called miter gates , was invented by Leonardo da Vinci sometime around the late 15th century. This reduces any leaks from between them and prevents their being opened until water levels have equalised. If the chamber is not full, the top gate is secure; and if the chamber is not completely empty, the bottom gate is secure in normal operation, therefore, the chamber cannot be open at both ends. A lower gate is taller than an upper gate, because the upper gate only has to be tall enough to close off the upper pound, while the lower gate has to be able to seal off a full chamber.
The upper gate is as tall as the canal is deep, plus a little more for the balance beam, winding mechanism, etc. A balance beam is the long arm projecting from the landward side of the gate over the towpath. As well as providing leverage to open and close the heavy gate, the beam also balances the non-floating weight of the gate in its socket, and so allows the gate to swing more freely.
A paddle � sometimes known as a slacker , clough , or in American English wicket � is the simple valve by which the lock chamber is filled or emptied. The paddle itself is a sliding wooden or nowadays plastic panel which when "lifted" slid up out of the way allows water to either enter the chamber from the upper pound or flow out to the lower pound. A gate paddle simply covers a hole in the lower part of a gate; a more sophisticated ground paddle blocks an underground culvert.
There can be up to 8 paddles two gate paddles and two ground paddles at both upper and lower ends of the chamber but there will often be fewer. For a long period since the s it was British Waterways policy not to provide gate paddles in replacement top gates if two ground paddles existed. The reason for this was given as safety, since it is possible for an ascending boat to be swamped by the water from a carelessly lifted gate paddle.
However, without the gate paddles the locks are slower to operate and this has been blamed in some places for causing congestion. Since the late s the preferred method has been to retain or re-install the gate paddles and fit 'baffles' across them to minimise the risk of inundation.
On the old Erie Canal , there was a danger of injury when operating the paddles: water, on reaching a certain position, would push the paddles with a force which could tear the windlass or handle out of one's hands, or if one was standing in the wrong place, could knock one into the canal, leading to injuries and drownings. Winding gear is the mechanism which allows paddles to be lifted opened or lowered closed. Typically, a square-section stub emerges from the housing of the winding gear. This is the axle of a sprocket "pinion" which engages with a toothed bar "rack" attached by rodding to the top of the paddle.
A lock-keeper or member of the boat's shore crew engages the square socket of their windlass see below onto the end of the axle and turns the windlass perhaps a dozen times. This rotates the pinion and lifts the paddle. A pawl engages with the rack to prevent the paddle from dropping inadvertently while being raised, and to keep it raised when the windlass is removed, so that the operator can attend to other paddles.
Nowadays it is considered discourteous and wasteful of water to leave a paddle open after a boat has left the lock, but in commercial days it was normal practice. To lower a paddle the pawl must be disengaged and the paddle wound down with the windlass.
Dropping paddles by knocking the pawl off can cause damage to the mechanism; the paddle gear is typically made of cast iron and can shatter or crack when dropped from a height. In areas where water-wastage due to vandalism is a problem, for example the Birmingham Canal Navigations , paddle mechanisms are commonly fitted with vandal-proof locks nowadays rebranded "water conservation devices" which require the boater to employ a key before the paddle can be lifted.
The keys are officially known as "water conservation keys", but boaters usually refer to them as T-keys , from their shape; handcuff keys because the original locks, fitted on the Leeds and Liverpool Canal , resembled handcuffs; Leeds and Liverpool Keys after that canal; or simply Anti-Vandal Keys. During the s, British Waterways began to introduce a hydraulic system for operating paddles, especially those on bottom gates, which are the heaviest to operate.
A metal cylinder about a foot in diameter was mounted on the balance beam and contained a small oil-operated hydraulic pump. A spindle protruded from the front face and was operated by a windlass in the usual way, the energy being transferred to the actual paddle by small bore pipes.
The system was widely installed and on some canals it became very common. There turned out to be two serious drawbacks. It was much more expensive to install and maintain than traditional gear and went wrong more frequently, especially once vandals learned to cut the pipes.
Even worse, it had a safety defect, in that the paddle once in the raised position could not be dropped in an emergency, but had to be wound down, taking a good deal longer.
These factors led to the abandonment of the policy in the late s, but examples of it survive all over the system, as it is usually not removed until the gates need replacing, which happens about every twenty years. A windlass also variously 'lock handle', 'iron' or simply 'key' is a detachable crank used for opening lock paddles the word does not refer to the winding mechanism itself.
The simplest windlass is made from an iron rod of circular section, about half an inch in diameter and two feet long, bent to make an L-shape with legs of slightly different length. The shorter leg is called the handle, and the longer leg is called the arm. Welded to the end of the arm is a square, sometimes tapered, socket of the correct size to fit onto the spindle protruding from lock winding gear.
On the Chesapeake and Ohio Canal, the lockkeepers were required to remove the windlasses from all lock paddles at night, to prevent unauthorized use. It is used more often to refer to a lock being filled or emptied for the benefit of someone else "The lock was turned for us by a boat coming the other way" and sometimes the opposite "The lock was set for us, but the crew of the boat coming the other way turned it before we got there".
A swell was caused by opening suddenly the paddle valves in the lock gates, or when emptying a lock. In one case, a boatsman asked for a back swell, that is, open and shut the paddles a few times to create some waves, to help him get off the bank where he was stuck. On the Erie Canal, some loaded boats needed a swell to get out of the lock, particularly lumber boats, being top heavy, would list to one side and get stuck in the lock, and needed a swell to get them out.
Some lockkeepers would give a swell to anyone to help them on the way, but some would ask for money for the swell. The Erie Canal management did not like swelling for two reasons.
First, it used too much water lowering the water on the pound above sometimes causing boats to run aground. In addition, it raised the water level on the pound below causing some boats to strike bridges or get stuck. The barge would be directed to the slack water to one side of the lock gates and as the volume of water decreased as the lock emptied the barge or boat is effectively sucked out of the slack water into the path of the lock gates.
The effort required to navigate the barge or boat into the mouth of the lock was therefore substantially reduced. On horse-drawn and mule-drawn canals, snubbing posts were used to slow or stop a boat in the lock. A ton boat moving at a few miles an hour could destroy the lock gate. To prevent this, a rope was wound around the snubbing post as the boat entered the lock.
Pulling on the rope slowed the boat, due to the friction of the rope against the post. Flagg and its drunk captain. That boat was already leaking; the crew, having partially pumped the water out, entered Lock 74, moving in front of another boat. Because they failed to snub the boat, it crashed into and knocked out the downstream gates. The outrush of water from the lock Boat Travelling Upstream And Downstream To caused the upstream gates to slam shut, breaking them also, and sending a cascade of water over the boat, sinking it.
This suspended navigation on the canal for 48 hours until the lock gates could be replaced and the boat removed from the lock. On most English narrow canals, the upper end of the chamber is closed by a single gate the full width of the lock. This was cheaper to construct and is quicker to operate with a small crew, as only one gate needs to be opened.
These were often fitted with a post allowing a rope to be used to stop the boat and close the gate at the same time. Some narrow locks e. They have single gates at the lower end also.
This speeds up passage, even though single lower gates are heavy heavier than a single upper gate, because the lower gate is taller and the lock has to be longer a lower gate opens INTO the lock, it has to pass the bow or stern of an enclosed boat, and a single gate has a wider arc than two half-gates. Some manually operated paddles do not require a detachable handle windlass because they have their handles ready-attached. On the Leeds and Liverpool Canal there is a variety of different lock gear.
Some paddles are raised by turning what is in effect a large horizontal wing nut butterfly nut lifting a screw-threaded bar attached to the top of the paddle. Others are operated by lifting a long wooden lever, which operates a wooden plate which seals the culvert. These are known locally as "jack cloughs".
Bottom gate paddles are sometimes operated by a horizontal ratchet which also slides a wooden plate sideways, rather than the more common vertical lift. Many of these idiosyncratic paddles have been "modernised" and they are becoming rare. On the Calder and Hebble Navigation , some paddle gear is operated by repeatedly inserting a Calder and Hebble Handspike length of 4" by 2" hardwood into a ground-level slotted wheel and pushing down on the handspike to rotate the wheel on its horizontal axis.
On some parts of the Montgomery Canal bottom paddles are used in place of side paddles. Rather than passing into the lock through a culvert around the side of the lock gate, the water flows through a culvert in the bottom of the canal. The paddle slides horizontally over the culvert. To economise, especially where good stone would be prohibitively expensive or difficult to obtain, composite locks were made, i.
This was done, for instance, on the Chesapeake and Ohio Canal with the locks near the Paw Paw Tunnel [21] and also the Chenango Canal [22] Because the wood would swell making the lock space smaller or rot away, the wood was often replaced by concrete.
Some locks are operated or at least supervised by professional or volunteer lock keepers. This is particularly true on commercial waterways, or where locks are large or have complicated features that the average leisure boater may not be able to operate successfully. For instance, although the Thames above Teddington England is almost entirely a leisure waterway, the locks are usually staffed.
Only recently have boaters been allowed limited access to the hydraulic gear to operate the locks when the keeper is not present. On large modern canals, especially very large ones such as ship canals , the gates and paddles are too large to be hand operated, and are operated by hydraulic or electrical equipment. On the Caledonian Canal the lock gates were operated by man-powered capstans , one connected by chains to open the gate and another to draw it closed.
By these had been replaced by hydraulic power acting through steel rams. On the River Thames below Oxford all the locks are staffed and powered. Powered locks are usually still filled by gravity, though some very large locks use pumps to speed things up. The construction of locks or weirs and dams on rivers obstructs the passage of fish. Some fish such as lampreys, trout and salmon go upstream to spawn.
Measures such as a fish ladder are often taken to counteract this. Navigation locks have also potential to be operated as fishways to provide increased access for a range of biota. A weigh lock is a specialized canal lock designed to determine the weight of barges to assess toll payments based upon the weight and value of the cargo carried. The Lehigh Canal also had weigh locks see photo on right. Loosely, a flight of locks is simply a series of locks in close-enough proximity to be identified as a single group.
For many reasons, a flight of locks is preferable to the same number of locks spread more widely: crews are put ashore and picked up once, rather than multiple times; transition involves a concentrated burst of effort, rather than a continually interrupted journey; a lock keeper may be stationed to help crews through the flight quickly; and where water is in short supply, a single pump can recycle water to the top of the whole flight.
The need for a flight may be determined purely by the lie of the land, but it is possible to group locks purposely into flights by using cuttings or embankments to "postpone" the height change. Examples: Caen Hill locks, Devizes. A set of locks is only a staircase if successive lock chambers share a gate i. Most flights are not staircases, because each chamber is a separate lock with its own upper and lower gates , there is a navigable pound however short between each pair of locks, and the locks are operated in the conventional way.
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