Applications for mass flow measurement include custody transfer (where a fluid product is bought or sold by its mass), chemical reaction processes (where the mass flow rates of reactants must be maintained in precise proportion in order for the desired chemical reactions to occur), and steam boiler control systems (where the out-flow of vaporous steam must be balanced by an equivalent in-flow of liquid water to the boiler – here, volumetric comparisons of steam and water flow would be useless because one cubic foot of steam is certainly not the same number of H2O molecules as one cubic foot of water). energy (pe), and flow work (wflow). Chapter In many situations, including in the cardiovascular system, branching of the flow occurs. What is Positive Displacement Flow Meter ? For steady state in-compressible flow the Euler equation becomes. As the name suggest flow rate is the measure of a volume of liquid that moves in a certain amount of time. (a) What is the average speed of the river in the gorge? Moreover, in this topic, you will learn about the flow rate, flow rate formula, formula’s derivation, and solved example. Commons Attribution-Noncommercial-Share Alike 3.0 United States We can use the relationship between flow rate and speed to find both velocities. (b) What is this rate in m3/s ? (credit: RaviGogna, Flickr). Identify some substances that are incompressible and some that are not. 11. The inside volume of the house is equivalent to a rectangular solid 13.0 m wide by 20.0 m long by 2.75 m high. piston: It is of interest that the specific flow work is (The large number obtained is an overestimate, but it is still reasonable.). In steady flow systems we find mass accumulation in the control volume, thus we will find it Steady Flow The relationship between volume (V ) and mass (m) for a sample of fluid is its mass density (ρ): Similarly, the relationship between a volumetric flow rate (Q) and a mass flow rate (W) is also the fluid’s mass density (ρ): Solving for W in this equation leads us to a product of volumetric flow rate and mass density: A quick dimensional analysis check using common metric units confirms this fact. (The converse applies for flow out of a constriction into a larger-diameter region.). , The process is exactly reversible. Aircraft Jet Engines. When dealing with closed systems we found that The SI unit for flow rate is m3/s, but a number of other units for Q are in common use. (b) What is the average speed of the water in the river downstream of the falls when it widens to 60 m and its depth increases to an average of 40 m? 4. We will only consider When a tube narrows, the same volume occupies a greater length. sketching T-v or P-v In this situation, continuity of flow is maintained but it is the sum of the flow rates in each of the branches in any portion along the tube that is maintained. 14. The nozzle produces a considerably faster stream merely by constricting the flow to a narrower tube. where n1 and n2 are the number of branches in each of the sections along the tube. Save my name, email, and website in this browser for the next time I comment. figure. In this course we consider three types of Control This is called the equation of continuity and is valid for any incompressible fluid. (c) What is unreasonable or inconsistent about the premises? Flow rate and velocity are related, but quite different, physical quantities. conditions throughout, in which there is no energy or rather than energy [kJ]. In active muscle, one finds about 200 capillaries per mm3, or about 200 × 106 per 1 kg of muscle. Blood is pumped from the heart at a rate of 5.0 L/min into the aorta (of radius 1.0 cm). 3. In this case, because the cross-sectional area of the pipe decreases, the velocity must necessarily increase. Substituting the known values (converted to units of meters and seconds) gives, Using ${n}_{1}{A}_{1}{\overline{v}}_{1}={n}_{2}{A}_{2}{\overline{v}}_{1}\\$, assigning the subscript 1 to the aorta and 2 to the capillaries, and solving for n2 (the number of capillaries) gives ${n}_{2}=\frac{{n}_{1}{A}_{1}{\overline{v}}_{1}}{{A}_{2}{\overline{v}}_{2}}\\$. Explain the consequences of the equation of continuity. pump. if we had a venturi tube generating a differential pressure of 2.30 kilopascals (kPa) at a mass flow rate of 500 kilograms per minute of naphtha (a petroleum product having a density of 0.665 kilograms per liter), we could solve for the k value of this venturi tube as such: Now that we know a value of 404.3 for k will yield kilograms per minute of liquid flow through this venturi tube given pressure in kPa and density in kilograms per liter, we may readily predict the mass flow rate through this tube for any other pressure drop and fluid density we might happen to encounter. The value of 404.3 for k relates the disparate units of measurement for us: As with volumetric flow calculations, the calculated value for k neatly accounts for any set of measurement units we may arbitrarily choose. where V is the volume and t is the elapsed time. For 20 kg of muscle, this amounts to about 4 × 109 capillaries. Note that a liter (L) is 1/1000 of a cubic meter or 1000 cubic centimeters (10-3 m3 or 103 cm3). Here the shaded cylinder of fluid flows past point P in a uniform pipe in time t. The volume of the cylinder is Ad and the average velocity is $\overline{v}=d/t\\$ so that the flow rate is $Q=\text{Ad}/t=A\overline{v}\\$ . Figure 1 illustrates how this relationship is obtained. This low speed is to allow sufficient time for effective exchange to occur although it is equally important for the flow not to become stationary in order to avoid the possibility of clotting.