Thank you for registering with Physics World If you'd like to change your details at any time, please visit My account. Blood may be thicker than water, but in a narrow enough tube, both liquids flow like treacle. This sluggish behaviour arises because, as you reduce the size of the channel, friction between the liquid and the channel wall comes to dominate the flow dynamics.
Researchers have tried various ways of engineering surfaces to reduce this effect, but now a team from France, Switzerland and Ireland has gone a step further by doing away with solid channel walls altogether. Instead, the researchers confine their fluid within a conduit that itself consists of a liquid. Writing in Nature , Peter Dunne University of Strasbourg , Takuji Adachi University of Strasbourg and University of Geneva and colleagues describe how they form the walls of their conduit using ferrofluid — a colloidal suspension of magnetic nanoparticles in oil.
The researchers outlined the shape of their desired channel using long, rod-shaped neodymium magnets held in a 3D-printed framework.
With four such magnets arranged with alternating polarities around the channel, they created a quadrupolar magnetic field whose strength fell to zero at the centre.
The ease with which a fluid flows over a surface is described by the slip length. In fluids that interact with the channel wall, flow is fastest at the centre and decreases along an approximately parabolic trend towards the solid—liquid interface.
The slip length defines the distance beyond this interface at which the flow velocity would fall to zero. A fluid that is held stationary at the channel edge has a slip length of zero, while longer slip lengths indicate more freely flowing fluids.
That, at least, is the case when the sides of the channel are solid and immovable. In the experiments reported by Dunne and Adachi, the magnetic fluid making up the conduit walls moves too, flowing along with the water near the centre of the channel, and recirculating back to the start along the outside edge, next to the magnets. This results in an effective slip length much longer than could be achieved if the conduit walls were static.
Many figures in the text show streamlines. Explain why fluid velocity is greatest where streamlines are closest together. Hint: Consider the relationship between fluid velocity and the cross-sectional area through which it flows.
The heart of a resting adult pumps blood at a rate of 5. Blood is pumped from the heart at a rate of 5. Determine the speed of blood through the aorta. Determine the flow rate and the volume that passes through the artery in a period of 30 s. At the gorge, the river narrows to 20 m wide and averages 20 m deep. Figure 3. A major artery with a cross-sectional area of 1. By what factor is the average velocity of the blood reduced when it passes into these branches?
If the blood speed increases by a factor of 4. The flow rate of blood through a 2. This small speed allows time for diffusion of materials to and from the blood. The large number obtained is an overestimate, but it is still reasonable.
The main uptake air duct of a forced air gas heater is 0. The inside volume of the house is equivalent to a rectangular solid Water is moving at a velocity of 2. Prove that the speed of an incompressible fluid through a constriction, such as in a Venturi tube, increases by a factor equal to the square of the factor by which the diameter decreases. The converse applies for flow out of a constriction into a larger-diameter region.
Water emerges straight down from a faucet with a 1. Because of the construction of the faucet, there is no variation in speed across the stream. Neglect any effects due to surface tension. Unreasonable Results A mountain stream is Skip to main content. Search for:. Define units of volume. Describe incompressible fluids. Explain the consequences of the equation of continuity. Example 1. Calculating Volume from Flow Rate: The Heart Pumps a Lot of Blood in a Lifetime How many cubic meters of blood does the heart pump in a year lifetime, assuming the average flow rate is 5.
Strategy Time and flow rate Q are given, and so the volume V can be calculated from the definition of flow rate. Example 2. Strategy We can use the relationship between flow rate and speed to find both velocities. This is a consequence of the continuity equation. If the flow Q is held constant, when the area A decreases, the velocity v must increase proportionally.
For example, if the nozzle of the hose is half the area of the hose, the velocity must double to maintain the continuous flow. Privacy Policy. Skip to main content. Search for:. Fluids in Motion. Flow Rate and the Equation of Continuity The flow rate of a liquid is how much liquid passes through an area in a given time. Learning Objectives Determine the flow rate based on velocity and area or elapsed time and justify the use of continuity in expressing properties of a fluid and its motion.
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