Translated 2.1.34-2.1.47

astrosander edited Sep 23, 2024, 3:40 AM

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		+	<meta name="description" content="The drag force of a liquid or gas, proportional to the square of the velocity of a moving body, is associated with the formation of vortices in the medium near the surface of this body. The drag force, which is proportional to the speed of a moving body, is associated with the slippage of the layers of the medium when it flows around this body. Both phenomena occur simultaneously. Why, however, can only one type of resistance be taken into account under certain conditions? Based on the data of the previous two problems, estimate at what value the product of the radius of a round drop and its velocity is, both types of air resistance are comparable in their effect on the movement of the drop.">
		+	<meta name="author" content="Aliaksandr Melnichenka">
		+	<meta name="date" content="2023-10" scheme="YYYY-MM">
		+	<meta property="og:title" content="The drag force of a liquid or gas, proportional to the square of the velocity of a moving body, is associated with the formation of vortices in the medium near the surface of this body. The drag force, which is proportional to the speed of a moving body, is associated with the slippage of the layers of the medium when it flows around this body. Both phenomena occur simultaneously. Why, however, can only one type of resistance be taken into account under certain conditions? Based on the data of the previous two problems, estimate at what value the product of the radius of a round drop and its velocity is, both types of air resistance are comparable in their effect on the movement of the drop.">
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		+	<meta property="og:description" content="The drag force of a liquid or gas, proportional to the square of the velocity of a moving body, is associated with the formation of vortices in the medium near the surface of this body. The drag force, which is proportional to the speed of a moving body, is associated with the slippage of the layers of the medium when it flows around this body. Both phenomena occur simultaneously. Why, however, can only one type of resistance be taken into account under certain conditions? Based on the data of the previous two problems, estimate at what value the product of the radius of a round drop and its velocity is, both types of air resistance are comparable in their effect on the movement of the drop.">
		+	<meta name="yandex-verification" content="6cfda41f74038368">
		+	<title>The drag force of a liquid or gas, proportional to the square of the velocity of a moving body, is associated with the formation of vortices in the medium near the surface of this body. The drag force, which is proportional to the speed of a moving body, is associated with the slippage of the layers of the medium when it flows around this body. Both phenomena occur simultaneously. Why, however, can only one type of resistance be taken into account under certain conditions? Based on the data of the previous two problems, estimate at what value the product of the radius of a round drop and its velocity is, both types of air resistance are comparable in their effect on the movement of the drop.</title>
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		+	<header style="text-align:center;">
		+	<div id = "logo">
		+	<span><img src = "../../img/book.png"><span><span>Savchenko Solutions</span>
		+	</div>
		+	<p class="author">
		+	Solutions of Savchenko Problems in Physics <br>
		+	<i><b>knowledge must be free</b></i>
		+	</p>
		+	</header>
		+
		+	<h3 id="back-link"><a href="../../#2.1">$\leftarrow$Back</a></h3>
		+
		+	<h3> Statement </h3>
		+	<p>
		+	$2.1.39^*.$ The drag force of a liquid or gas, proportional to the square of the velocity of a moving body, is associated with the formation of vortices in the medium near the surface of this body. The drag force, which is proportional to the speed of a moving body, is associated with the slippage of the layers of the medium when it flows around this body. Both phenomena occur simultaneously. Why, however, can only one type of resistance be taken into account under certain conditions? Based on the data of the previous two problems, estimate at what value the product of the radius of a round drop and its velocity is, both types of air resistance are comparable in their effect on the movement of the drop.
		+	</p>
		+
		+	<h3>Solution</h3>
		+	<p>
		+	<p>
		+	This is related to the Reynolds number for a given situation.
		+	</p>
		+	<p>
		+	If the Reynolds number $\text{Re}<2000$, then the drag force is proportional to the speed
		+	</p>
		+	<p>
		+	If $\text{Re}>2000$, then the drag force is proportional to the square of the speed
		+	</p>
		+	<p>
		+	NO: More about Reynolds numbers <a href="https://en.wikipedia.org/wiki/Reynolds_number" target="_blank">wikipedia.org</a>
		+	</p>
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			<meta name="keywords" content="Savchenko Problems in Physics, Savchenko solutions, physics problems, physics olympiad preparation, IPhO, Jaan Kalda">
			<meta name="description" content="The drag force of a liquid or gas, proportional to the square of the velocity of a moving body, is associated with the formation of vortices in the medium near the surface of this body. The drag force, which is proportional to the speed of a moving body, is associated with the slippage of the layers of the medium when it flows around this body. Both phenomena occur simultaneously. Why, however, can only one type of resistance be taken into account under certain conditions? Based on the data of the previous two problems, estimate at what value the product of the radius of a round drop and its velocity is, both types of air resistance are comparable in their effect on the movement of the drop.">
			<meta name="author" content="Aliaksandr Melnichenka">
			<meta name="date" content="2023-10" scheme="YYYY-MM">
			<meta property="og:title" content="The drag force of a liquid or gas, proportional to the square of the velocity of a moving body, is associated with the formation of vortices in the medium near the surface of this body. The drag force, which is proportional to the speed of a moving body, is associated with the slippage of the layers of the medium when it flows around this body. Both phenomena occur simultaneously. Why, however, can only one type of resistance be taken into account under certain conditions? Based on the data of the previous two problems, estimate at what value the product of the radius of a round drop and its velocity is, both types of air resistance are comparable in their effect on the movement of the drop.">
			<meta property="og:image" content="img/logo.png">
			<meta property="og:description" content="The drag force of a liquid or gas, proportional to the square of the velocity of a moving body, is associated with the formation of vortices in the medium near the surface of this body. The drag force, which is proportional to the speed of a moving body, is associated with the slippage of the layers of the medium when it flows around this body. Both phenomena occur simultaneously. Why, however, can only one type of resistance be taken into account under certain conditions? Based on the data of the previous two problems, estimate at what value the product of the radius of a round drop and its velocity is, both types of air resistance are comparable in their effect on the movement of the drop.">
			<meta name="yandex-verification" content="6cfda41f74038368">
			<title>The drag force of a liquid or gas, proportional to the square of the velocity of a moving body, is associated with the formation of vortices in the medium near the surface of this body. The drag force, which is proportional to the speed of a moving body, is associated with the slippage of the layers of the medium when it flows around this body. Both phenomena occur simultaneously. Why, however, can only one type of resistance be taken into account under certain conditions? Based on the data of the previous two problems, estimate at what value the product of the radius of a round drop and its velocity is, both types of air resistance are comparable in their effect on the movement of the drop.</title>
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			</head>
			<body style="">
			<header style="text-align:center;">
			<div id = "logo">
			<span><img src = "../../img/book.png"><span><span>Savchenko Solutions</span>
			</div>
			<p class="author">
			Solutions of Savchenko Problems in Physics <br>
			<i><b>knowledge must be free</b></i>
			</p>
			</header>

			<h3 id="back-link"><a href="../../#2.1">$\leftarrow$Back</a></h3>

			<h3> Statement </h3>
			<p>
			$2.1.39^*.$ The drag force of a liquid or gas, proportional to the square of the velocity of a moving body, is associated with the formation of vortices in the medium near the surface of this body. The drag force, which is proportional to the speed of a moving body, is associated with the slippage of the layers of the medium when it flows around this body. Both phenomena occur simultaneously. Why, however, can only one type of resistance be taken into account under certain conditions? Based on the data of the previous two problems, estimate at what value the product of the radius of a round drop and its velocity is, both types of air resistance are comparable in their effect on the movement of the drop.
			</p>

			<h3>Solution</h3>
			<p>
			<p>
			This is related to the Reynolds number for a given situation.
			</p>
			<p>
			If the Reynolds number $\text{Re}<2000$, then the drag force is proportional to the speed
			</p>
			<p>
			If $\text{Re}>2000$, then the drag force is proportional to the square of the speed
			</p>
			<p>
			NO: More about Reynolds numbers <a href="https://en.wikipedia.org/wiki/Reynolds_number" target="_blank">wikipedia.org</a>
			</p>
			<footer class="row container">
			<br>
			<p>
			<small> © <strong>Savchenko Solutions</strong>, 2023-2024 <br></small>
			</p>
			<p>
			<small>All rights belong to the authors. <br> Commercial use of materials - with the written permission of the authors. <br> alex@savchenkosolutions.com <br></small>
			</p>
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