Speed of stream formula

Boats and Streams is an essential topic for many competitive exams. Many varieties of questions can be framed from this area. We use the fundamental concepts of time speed and distance only to solve elementary questions on Boats and Streams. However, some types of questions are tricky and take lots of time to solve by applying textbook approach. Fortunately, there are some shortcut formulas available to handle such problems. In this article, besides an understanding of the basic concepts of boat sand streams, we will also learn few tricks to solve some exceptional questions. Boats and Streams – Terminologies: Stream: It implies that the water in the river is moving or flowing. Downstream or with the stream: It indicates that the stream favors the man’s rowing (or boating). i.e., the direction of rowing and direction of flow (stream) is same. Upstream or against the stream: It indicates that the stream flows against the man’s rowing (or boating), i.e., the direction of rowing and direction of the stream (current) are opposite. Some shortcut formulas related to the speed of boats and streams is handy as we require them frequently. Below are the lists of the formulas: Let the speed of a boat (or man) in still water be X m/sec, and the speed of the stream (or current) be Y m/sec. • Speed of boat with the stream (or Downstream or D/S) = (X + Y) m/sec. • Speed of boat against the stream (or Upstream or D/S) = (X – Y) m/sec. • Speed of man/boat in still water = • Speed of the str...

Stream Processes Stream Flow and Sediment Transport Stream velocity is the speed of the water in the stream. Units are distance per time (e.g., meters per second or feet per second). Stream velocity is greatest in midstream near the surface and is slowest along the stream bed and banks due to friction. Hydraulic radius (HR or just R) is the ratio of the cross-sectional area divided by the wetted perimeter. For a hypothetical stream with a rectangular cross sectional shape (a stream with a flat bottom and vertical sides) the cross-sectional area is simply the width multiplied by the depth (W * D). For the same hypothetical stream the wetted perimeter would be the depth plus the width plus the depth (W + 2D). The greater the cross-sectional area in comparison to the wetted perimeter, the more freely flowing will the stream be because less of the water in the stream is in proximity to the frictional bed. So as hydraulic radius increases so will velocity (all other factors being equal). Stream discharge is the quantity (volume) of water passing by a given point in a certain amount of time. It is calculated as Q = V * A, where V is the stream velocity and A is the stream's cross-sectional area. Units of discharge are volume per time (e.g., m 3/sec or million gallons per day, mgpd). At low velocity, especially if the stream bed is smooth, streams may exhibit laminar flow in which all of the water molecules flow in parallel paths. At higher velocities turbulence is introduced int...

\( \newcommand\) • • • • • • • • • • • • • • • • • • • • • • Traffic Flow is the study of the movement of individual drivers and vehicles between two points and the interactions they make with one another. Unfortunately, studying traffic flow is difficult because driver behavior cannot be predicted with one-hundred percent certainty. Fortunately, drivers tend to behave within a reasonably consistent range; thus, traffic streams tend to have some reasonable consistency and can be roughly represented mathematically. To better represent traffic flow, relationships have been established between the three main characteristics: (1) flow, (2) density, and (3) velocity. These relationships help in planning, design, and operations of roadway facilities. Time-Space Diagram Traffic engineers represent the location of a specific vehicle at a certain time with a time-space diagram. This two-dimensional diagram shows the trajectory of a vehicle through time as it moves from a specific origin to a specific destination. Multiple vehicles can be represented on a diagram and, thus, certain characteristics, such as flow at a certain site for a certain time, can be determined. Flow and density Flow (q) = the rate at which vehicles pass a fixed point (vehicles per hour) , \[ t_ • \(q\) = equivalent hourly flow • \(L\) = length of roadway • \(k\) = density Time-space diagram showing trajectories of vehicles over time and space Relating time and space mean speed Note that the time mean speed is ...

Learning Objectives By the end of this section, you will be able to: • Calculate flow rate. • Define units of volume. • Describe incompressible fluids. • Explain the consequences of the equation of continuity. Flow rate \(Q\) is defined to be the volume of fluid passing by some location through an area during a period of time, as seen in Figure \(\PageIndex\). Example \(\PageIndex\): When a tube narrows, the same volume occupies a greater length. For the same volume to pass points 1 and 2 in a given time, the speed must be greater at point 2. The process is exactly reversible. If the fluid flows in the opposite direction, its speed will decrease when the tube widens. (Note that the relative volumes of the two cylinders and the corresponding velocity vector arrows are not drawn to scale.) Since liquids are essentially incompressible, the equation of continuity is valid for all liquids. However, gases are compressible, and so the equation must be applied with caution to gases if they are subjected to compression or expansion. Example \(\PageIndex_2,\] where \(n_1\) and \(n_2\) are the number of branches in each of the sections along the tube. Example \(\PageIndex\] Discussion Note that the speed of flow in the capillaries is considerably reduced relative to the speed in the aorta due to the significant increase in the total cross-sectional area at the capillaries. This low speed is to allow sufficient time for effective exchange to occur although it is equally important for ...

Given: The speed of the boat in still water = 15 km/h Concept: Downstream speed of boat = Speed of boat in still water + Speed of stream Formula used: S = D/T(Where S = Speed, D = Distance, and T = Time) Calculation: ⇒ The speed of boat in downstream = 15 + 3 = 18 km/h = 18/60 km/minutes = 0.3 km/minutes ⇒ The distance travelled in 12 minutes in downstream = 0.3× 12 = 3.6 km ∴ The required result will be 3.6 km.

Question Download Solution PDF A boat travels from point P to point Q upstream and returns from point Q to point P downstream, PQ = 96 km. If the round trip takes 15 hours and the speed of the boat in still water is 8 km/h more than the speed of the stream, find the time taken for the downstream journey. GIVEN : Total time taken in the journey was 15 hours. Speed of the boat is 8 km/hr more than the speed of the stream. CONCEPT : Going along the stream= speed of the boat in still water + speed of the stream. Going against the stream = speed of the boat in still water - speed of the stream. FORMULA USED : s = v × t Where, s = distance of the journey, v = speed, t = time taken ASSUMPTION : Let’s take speed of the boat = \(v\)km/hr speed of the stream = \(x\)km/hr And, v – x = 8 ⇒ v = x + 8 Downstream speed = (v + x) km/hr = (2x + 8) km/hr Upstream speed = (v - x) km/hr = 8 km/hr CALCULATION : ATQ, \(\frac = 15 - 12 = 3\) ⇒ 2x + 8 = 32 ⇒ x = 12 Downstream speed = (2 × 12 + 8) = 32 km/hr Downstream journey time = 96/32 = 3 hours Students can also use the options to solve the question. In that case also equation (i) has to be determined. Then by looking at the option we can clearly see 3 hours is the answer.