# Poiseuille's law questions with answers

Recent questions in Poiseuille's Law

### For the electrical resistance of a conductor, we have$R=\rho \frac{l}{A}$Noting the structural similarity between the Hagen-Poiseuille law and Ohm's law, we can define a similar quantity for laminar flow through a long cylindrical pipe:${R}_{V}=8\eta \frac{l}{A{r}^{2}}$So there's a structural difference of a factor of ${r}^{2}$ between the two. What's the intuition behind this?

Carley Haley 2022-05-20 Answered

### Why is pressure gradient assumed to be constant with respect to radius in the derivation of Poiseuille's Law?Poiseuille's Law relies on the fact that velocity is not constant throughout a cross-section of the pipe (it is zero at the boundary due to the no-slip condition and maximum in the center). By Bernoulli's Law, this means that pressure is maximum at the boundary and minimum at the center. But in the book I have it is assumed that the pressure gradient is independent of radius (distance from the center of the pipe), and the pressure gradient is thus extricated from a radius-integral. Can anyone justify this?

Laila Andrews 2022-05-19 Answered

### How to convert this derivation of Poiseuille's law into the standard one?I am trying to derive Poiseuille's law. I have reached a point in the derivation where I have:$V=\frac{\left(p1-p2\right)\left({R}^{2}\right)}{4lu}$Where $l$ is length, u is viscosity, p is pressure, v is flow velocity and R is radius. What I am stuck on is shifting this to the volumetric flow rate:$V\pi {R}^{2}=Q=\frac{\left(p1-p2\right)\left({R}^{4}\right)}{4lu}.$$V\pi {R}^{2}=Q=\frac{\left(p1-p2\right)\left({R}^{4}\right)}{4lu}.$However this is incorrect as Poiseuille's law is divided by 8. I know that I am probably missing something obvious, but I can't think of a reason as to why the whole equation needs to be halved. Any help understanding why (or whether my original derivation for V was inaccurate) would be appreciated.

Brooklynn Hubbard 2022-05-18 Answered

### Hydraulic dynamics questionWe know the length of a pipe, say L, and the starting point pressure p1, ending point p2, cross-sectional area A. What else do we need to compute the mean velocity of flow in this pipe?My full question actually runs as follows. Given the mean cardiac output(volume flux) be 5.5L per min, the radius of the aorta is about 1.1cm. In the systemic circulatory system, the mean radius of a capillary is about 3µm. The mean pressure at the arterial end of the capillary bed (beginning of the capillary system) is estimated to be about 30mmHg, and about 15mmHg at the venous end (end of the capillary system). The length of capillary is 0.75mm.Calculate the mean velocity in the aorta and in a capillary.My idea is to use the volume flux 5.5L/min and the radius of aorta, divide the flux by the crossectional area to find the mean velocity in the aorta. However, I have no idea how to deal with the velocity in a capillary. I tried to use Poiseulle's law, but given that we only know the difference of pressure and length of the capillary, it is still unsolvable. Could anyone tell me how to deal with it?

Jordon Haley 2022-05-18 Answered

### Proving that the water leaving a vertical pipe is exponential (decay)How can I prove that the rate of which water leaves a vertical cylindrical container (through a hole at the bottom) is exponential of the form :$A{e}^{kx}$I know that Torricelli's law is:$\sqrt{2gh}$But this only proves a square root relationship. I have data points every 10 seconds and graphed it suggests a decay function. I know the distance between the pipe is 1.5M and the internal diameter is 5cm. The hole diameter is 0.25cm, if this helps. I need to prove that the water leaving the pipe is exponentially decaying.

Iyana Macdonald 2022-05-17 Answered

### What happens to pipe length when the pipe diameter changes?Intuitively, when the diameter of pipe is decreased, there will be more friction loss, more water pressure, and a higher flow rate. Is there a direct relationship/equation derived to see the affect of the pipe lengths?Deriving from Hagen-Poiseuille's equation, we get:where :$Q=$ flow rate change in fluid pressure$r=$ radius of pipe,$\mu =$ dynamic viscosity of fluid,$L=$ length of pipeTo keep similar flow rates, are we able to use Poiseuille's derived formula to find the new lengths of pipe with a change in $r$ (pipe radius)?

Edith Mayer 2022-05-17 Answered

### Why exactly is the resistance of a conductor inversely proportional to the area of its cross-section?Before I explain my query, I would like to clarify that I am a ninth-grader who got this question while studying the formula $R\propto \frac{1}{A}$ where $A$ is the area of cross-section.I have often asked this question to my teachers and they always give me the classic "corridor and field example". They told me that if 5 people walk in a corridor, they will find it harder to get across than if they were to be walking through a field- the same goes for electrons passing through a conductor. My counter-argument would be that if the width of the conductor increases, so will the number of positive ions (my textbook says that positive ions in conductors hinder the flow of current) and hence, more the resistance.I would really appreciate it if the answer could be explained to me in simple terms as I'm not well versed with the more complex formulae involved in this concept. If not, do let me know of the concepts I should read about (preferably the specific books) to understand the solution better.

Jayden Mckay 2022-05-15 Answered

### How does the radius of a pipe affect the rate of flow of fluid?Poiseuille's law states that the rate of flow of water is proportionate to ${r}^{4}$ where $r$ is the radius of the pipe. I don't see why.Intuitively I would expect rate of flow of fluid to vary with ${r}^{2}$ as the volume of a cylinder varies with ${r}^{2}$ for a constant length. The volume that flows past a point is equal to rate of flow fluid, and thus it should vary with ${r}^{2}$I cannot understand the mathematical proof completely. Is there an intuitive explanation for this?

Blaine Stein 2022-05-15 Answered

### Is there a contradiction between the continuity equation and Poiseuilles Law?The continuity equation states that flow rate should be conserved in different areas of a pipe:$Q={v}_{1}{A}_{1}={v}_{2}{A}_{2}=v\pi {r}^{2}$We can see from this equation that velocity and pipe radius are inversely proportional. If radius is doubled, velocity of flow is quartered.Another way I was taught to describe flow rate is through Poiseuilles Law:$Q=\frac{\pi {r}^{4}\mathrm{\Delta }P}{8\eta L}$So if I were to plug in the continuity equations definition of flow rate into Poiseuilles Law:$vA=v\pi {r}^{2}=\frac{\pi {r}^{4}\mathrm{\Delta }P}{8\eta L}$Therefore:$v=\frac{{r}^{2}\mathrm{\Delta }P}{8\eta L}$Now in this case, the velocity is proportional to the radius of the pipe. If the radius is doubled, then velocity is qaudrupled.What am I misunderstanding here? I would prefer a conceptual explanation because I feel that these equations are probably used with different assumptions/in different contexts.

Jay Barrett 2022-05-13 Answered

### Do you need to increase pressure to pump a fluid from a large pipe through a small pipe?The application of this question is towards clogged arteries and blood flow. I am wondering why people with clogged arteries have high blood pressure if a smaller artery (assuming it is smooth and cylindrical) means less pressure exerted by the blood according to Bernoulli's Equation. Is this because the heart has to pump the blood harder to be able to travel through a smaller arterial volume?

Matthew Hubbard 2022-05-10 Answered