12.1 Flow Rate and Its Relation to Velocity

12.1 Flow Rate and Its Relation to Velocity

• The most general applications of Bernoulli's Equation are calculated using Torricelli's theorem.

• Explain what it is.

• Explain how resistance affects pressure.

• The Reynolds number can be used to determine whether the system is turbulent or laminar.

• Determine the Reynolds number for an object moving through a fluid.

• The Reynolds number indicates turbulent flow or laminar flow.

• An object has a terminal speed.

• Many situations in which fluids are static have been dealt with by us.
• By their definition, fluids flow.
• A column of smoke from a camp fire, water streams from a fire hose, and blood courses through your veins are some examples.
• We can answer these and many other questions.

• The volume is the elapsed time.

• A number of other units are used in the same way as the SI unit for flow rate.
• A resting adult's heart pumps blood at a rate of 5000 liters per minute.

• Whatever metric units are most convenient for a given situation will be used in this text.

• The flow rate is the volume of fluid flowing past a point.

• The flow rate is determined by the volume of the cylinder and the average velocity.

• The volume can be calculated from the definition of the flow rate.

• The amount of blood is 200,000 tons.
• The volume of water contained in a 50-m lap pool is about 200 times the value.

• Physical quantities are different between flow rate and velocity.
• Think about the flow rate of the river.
• The size of the river affects the flow rate.
• The Amazon River in Brazil has more water than a rapid mountain stream.

• The equation seems logical.
• The relationship tells us that the flow rate is related to the size of the river and the average speed.

• The equation becomes.

• There is an incompressible fluid flowing along a pipe.
• The same amount of fluid must flow past any point in the tube in a given time because the fluid is incompressible.
• The cross-sectional area of the pipe must increase in order for the velocity to increase.
• It can be said that the flow rate must be the same at all points along the pipe.

• The equation of continuity is valid for any incompressible fluid.
• The consequences of the equation of continuity can be seen when the water in the hose comes into a spray nozzle with a large speed.
• When a river empties into one end of a reservoir, the water slows considerably, perhaps picking up speed again when it leaves the other end.

• The volume of the tube shrinks when it narrows.
• The speed must be greater at point 2 for the same volume to pass points 1 and 2 in a given time.
• The process can be reversed.
• When the tube widens, the fluid's speed will decrease.

• The equation of continuity is valid for all liquids since they are incompressible.
• If gases are subjected to compression or expansion, the equation must be applied with caution.

• Flow rate and speed can be used to find velocities.
• The subscript 1 is for the hose and the subscript 2 is for the nozzle.

• The equation of continuity will be used to give a different insight into the speed of the nozzle.

• It's about right for water to come from a nozzleless hose at a speed of 1.96 m/s.
• The faster stream is produced by the constriction of the flow to a narrower tube.

• The last part of the example shows that the speed of the tube is related to the square of the tube.
• By pursing our lips, we can blow out a candle at a distance, whereas blowing a candle with our mouth open is not very effective.

• In the cardiovascular system, branching of the flow occurs.
• The blood is pumped from the heart into arteries that divide into smaller arteries which branch into larger vessels called capillaries.
• The sum of the flow rates in each of the branches along the tube is what determines continuity of flow.

• The main blood vessel through which blood leaves the heart is called the aorta.
• There is a 10mm radius on the aorta.
• The speed of blood in the capillaries can be measured by the rate of blood flow in the aorta.
• The number of capillaries in the blood circulatory system is determined by the average diameter of a capillary.

• The general form of the equation of continuity can be used to calculate the number of capillaries, as all of the other variables are known.

• To assign the subscript 1 to the aorta and 2 to the capillaries, you have to solve for the number of capillaries.

• The total cross-sectional area at the capillaries has increased, which has reduced the speed of flow in the capillaries.
• It is equally important for the flow not to become stationary in order to avoid the possibility of clotting, but this low speed is to allow enough time for effective exchange to occur.
• One can find about 200 capillaries in active muscle.
• This is about 20 kilograms of muscle.