When you drink you beverage with a straw, you need to overcome both gravity and friction in the

When you drink you beverage with a straw, you need to...

Key Concepts

Laminar vs Turbulent Flow

This concept involves classifying the nature of fluid flow based on the Reynolds number, which compares inertial forces to viscous forces. In contexts like flow through a straw, if the Reynolds number is relatively low, the flow is laminar, meaning it is smooth and orderly. Understanding whether the flow is laminar or turbulent is essential because it affects the frictional losses experienced by the fluid.

Viscous Friction in Fluid Flow

When a fluid flows through a narrow channel like a straw, the internal friction (or viscosity) of the fluid creates a pressure drop along the length of the channel. This viscous friction can be analyzed using principles such as the Hagen-Poiseuille law in laminar flow, which quantifies the pressure drop based on viscosity, flow rate, channel length, and diameter. This concept is central in estimating how much effort is needed to overcome friction when drinking through a straw.

Gravitational Effects on Fluids

This concept deals with the potential energy difference a fluid must overcome to rise against gravity. Drinking through a straw requires creating a pressure difference that not only accelerates the liquid but also lifts it against gravitational pull. Estimating the gravitational contribution involves considering the height the liquid is raised, thereby determining the energy or pressure needed for this vertical displacement.

Pressure Differential Creation

This concept explains how a difference in pressure is generated, usually by reducing the pressure at the top of the straw when sucking. The pressure differential must be sufficient to overcome both the gravitational head and the frictional losses within the straw. It plays a crucial role in fluid dynamics by driving the flow from a region of higher pressure (atmospheric pressure) to one of lower pressure (inside the mouth).

Order-of-Magnitude Estimation

Order-of-magnitude estimation is a valuable technique in physics and engineering that allows one to approximate the relative contributions of different effects, such as gravitational forces versus frictional forces in this scenario. By making reasonable assumptions about parameters like liquid properties, straw dimensions, and drinking rate, one can develop an approximate ratio or fraction that highlights which factor contributes more significantly to the overall effort required to drink through a straw.

Transcript

00:01 We're asked about the pressure drop in a straw when you're using a straw to overcome both gravity and friction in the straw.

00:12 So when you drink a beverage.

00:14 So we want to estimate the fraction of the total effort you put into quenching your thirst of each factor, making suitable assumptions about the liquid and straw properties and your drake rate.

00:30 And we don't know is the flow laminar and turbulent, and we should ignore minor losses.

00:36 Okay, so we have a, we have bernoulli's equation, or conservation of energy.

00:46 Well, kind of conservation of energy.

00:48 We have losses here because of pipe friction, pipe losses.

00:57 Because of a friction factor here.

01:00 So what we have then is we're going to say, okay, well, the velocity at the start, and we're going to basically assume that there's no, the kinetic energy is roughly zero, just basically as a, you know, first approximation, you know, that at the inlet and the outlet of this draw, we have a zero velocity.

01:31 We'll take a reference pressure to be p1.

01:35 And then we have a change in height.

01:38 So that's the gravity portion.

01:41 And so then we have p2 where we have the pressure drop in basically the vacuum, pulling the fluid up the straw.

01:55 All right.

01:56 So we have our formula for the losses here.

02:02 And again, using, we'll have to, you know, look this guy up.

02:08 And this is basically going to be the flow in the pipe or in the straw.

02:13 Again, we're assuming that it's kind of, it's negligible at the start in the end.

02:18 But internally, then it's going to be, there's going to be flow, and there's going to be losses because of the friction in the pit.

02:27 Okay.

02:28 Okay.

02:29 So we have, so the pressure from gravity is just going to be then p, the pressure from gravity is minus row g times a change in height.

02:39 So basically how far you're pulling the fluid up the straw.

02:42 And then the pressure caused by friction that you need to overcome is then this guy here, times row, obviously, and with the minus sign.

02:55 So we have, that's the, uh, that's the, uh, friction pressure.

02:59 Now, now we need to make some assumptions.

03:03 So for a flow rate, a volumetric flow rate, anyway, we can say that let's say we can drink 12 fluid ounces in five seconds through this straw, which is through a straw, you're not shotgunning this.

03:21 So through a straw is, that's pretty quick, if you think about it.

03:29 And again, it obviously depends on how big the straw is.

03:33 So then we can do a bunch of unit conversions, get it in the gallons, then get in the cubic feet.

03:40 And so we wind up with 2 .51 times 10 to minus 3 cubic feet per second or fluid flowing through that pipe or the straw.

03:52 Now, we're going to say the length of the straw is, inches roughly that seems a little short term...

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