A hypodermic syringe contains a medicine with the density of...

Key Concepts

Pressure

Pressure is defined as the force applied per unit area and is a fundamental concept in fluid mechanics. In practical applications, such as in a syringe, applying a force over a specific area increases the pressure in the fluid, which in turn causes the fluid to move from regions of higher pressure to regions of lower pressure.

Bernoulli's Principle

Bernoulli's Principle states that for an incompressible, non-viscous fluid in steady flow, the total mechanical energy (which includes pressure energy, kinetic energy, and potential energy) is conserved along a streamline. This principle is used to relate the pressure difference created by an applied force to the velocity of the fluid as it exits an opening.

Continuity Equation

The continuity equation reflects the conservation of mass in fluid dynamics. For an incompressible fluid, the product of the cross-sectional area and the velocity must remain constant along the flow path. This concept ensures that even when a fluid passes through regions of differing cross-sectional areas, such as from a syringe barrel to a needle, the flow rate remains constant.

Fluid Density

Fluid density is the mass per unit volume of a fluid and is a critical parameter when relating pressure differences to fluid acceleration. In applying Bernoulli's Principle, the density of the fluid is used to calculate the conversion of pressure energy into kinetic energy, thereby determining the speed of the fluid as it exits.

Transcript

00:01 All right, so we have a siri's.

00:05 So something like that, it has a wider side with cross sectional area.

00:10 Uppercase it.

00:12 Okay.

00:13 And, um, and the narrower side with a cross sectional area is lower case, all right, on this city's country in some medicine.

00:26 And the density of the medicine is basically the same as the density off water.

00:32 All right? and when there is no force applied anywhere, then the pressure just atmospheric pressure.

00:44 Unless it up, that is just p zero.

00:47 So everywhere it is that most eric pressure on that s p zero.

00:52 Ok, but suppose we have a force applied to this blangger.

00:58 Okay.

00:58 And let's say that is if okay, so what happened? um, because of this force, there will be squared off medicine toe through this narrower side.

01:12 Okay, now, the question asked, what is the velocity v ah.

01:21 At this point, i'm into the through the narrower side when you apply, therefore safe through the wider side.

01:29 Okay, so now you know that when you applied a force through through this bangor all right, the in this side, the pressure is no longer that most very pressure.

01:41 The pressure will be p zero, right? atmospheric pressure class, the pressure due to dis apply force and that it just if over e right, on the other hand, in this side, the pressure in just this that most very pressure because there is no applied force over there.

02:07 Okay, but how to calculate the velocity of this side? okay, to do that, that usefully question is the battle is a question.

02:20 I mean, you have to apply.

02:21 Ah, barn barn.

02:23 Elissa question to solve this problem.

02:25 Okay.

02:26 And the question is, what is the bernoulli's equation? so bernoulli's equation, if you remember the barn eliza question said that if the liquid inside is is an ideal liquid than, um, pressure at any point of these syrians ah, i mean, the some of the pressure on the kinda tick nrg fire unit volume at that point.

02:58 And the potential energy part of need volume at that point is constant.

03:03 What it means is the pressure current energy per unit volume and important shell and agip, a unit volume will be constant at any point.

03:13 Um, for these syrians, i mean for this liquid basically.

03:18 Okay, so what s so if i write down the equation.

03:23 I can write it something like that.

03:25 So the burn eliza questions basically pressure.

03:29 Plus the kind knittig energy party.

03:34 You need volume and i did just half rule v square plus the potential energy per unit volume.

03:47 And that this role june why? and these quell toe constant okay, let's say constant equal to see.

03:58 Okay, now you can ride these a question for left side.

04:04 I mean, for the wider side and for the no words like separately and equal.

04:10 Damn.

04:10 Okay, so if you do that, then you re question is something like that p one plus huff room v one square plus rule z.

04:33 Why juan? okay.

04:37 And that is ah, this expression.

04:41 I mean, what i wrote down so far is the expression for the wider side and the same thing.

04:48 We can write for the narrower side.

04:50 And that should be something like that.

04:52 P two glass half rule v two square plus room, do you? why? to right, so that is basically down.

05:16 Ah, barn willis equation.

05:18 And the left hand side is for the wider side.

05:20 And the right hand side is for the narrower side.

05:23 Okay, now, um, now, if this is the thing.

05:32 This line is the reference line.

05:37 Okay, then you can see that.

05:40 Why it is this distance.

05:43 I mean, this height from this reference line.

05:45 Okay? and why? sorry? this is why one, right? andi? this is why too, right? so why one and why? to basically the same thing, right? that that's why the roads ey one.

06:08 I mean the grave additional important shell energy per unit volume at the wider side is equal to the grave.

06:16 Additional bottom shell energy.

06:18 Our unit volume at the narrower side.

06:21 So this time and this time, cancel out.

06:24 Okay.

06:26 All right.

06:27 Very good.

06:29 So then our equation is little bit simpler, right? p one.

06:37 But now, instead of writing p one, let me write down p zero plus f over a right to make the ah equation more singler.

06:53 Right.

06:55 And then half rule on v one square where everyone is the velocity of the wider side.

07:04 Okay.