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物理 大学生・専門学校生・社会人

流体力学の最初の最初、ラグランジュ微分のところでつまづいて困っております。 二枚目の?をつけた計算過程はどのような微分なのでしょうか? よろしくお願いします。

の1 流れの運動学 8 1 = (u.V)u U のようにして得られた. 記号▽はナブラ (nabla) とよみ 0 鶏分(1.14) 0 マ= e』 + ey Oy 0z のように定義される演算子 (operator) であるす. ea, ey. Ez はそれぞれ』軸, 軸,2軸の正の向きに向かう単位ベクトル (unit vector) で, これらを基本ベク トル (fundamental unit vector)という。 式(1.12) の両辺を At でわって, At →0 の極限をとると,流体粒子の受け る加速度a(z,t) を求めることができ に Au a(x, t) = lim + (u-V) u(z, t) At→0 At Ot D -u(x,t) Dt となる.ただし D +u.V Ot Dt で,D/Dt をラグランジュ微分 (Lagrangian derivative),あるいは実質微 分(substantial derivative), あるいは物質微分 (material derivative) という。 Du/Dt= Ou/0t+ (u.V)uの右辺第1項は, 流体中のある点aをつぎつぎと 通過する流体粒子の速度の時間的変化の割合を表しており,局所加速度 (local acceleration) とよばれている. また第2項は,点cにある流体粒子がある瞬間 にその前後の流体粒子の速度差のために受ける速度の時間的変化割合で対流加 速度 (convective acceleration) とよばれている。 ラグランジュ微分 D/Dtは, オイラーの方法の意味で »とtの関数として表 された量,すなわち 「場の量」に対してのみ作用させることができる. なぜな ら,その定義式(1.16) の右辺は, 独立変数を αとtとするときの偏微分0/0tと ▽によって構成されているからである. aとtの任意関数 f(z,t) のラグラン ジュ微分は,式(1.15) を導いた過程から理解できるように, 流れに伴う f(x.t) の時間的変化の割合,すなわち, 流体粒子の軌跡に沿っての f(z,t) の時間的変 化の割合を表す。 十演算子▽をスカラー関数f(a)に作用させて得られるVfは, f の勾配 (gradient) とよばれ る。▽をスカラー関数に作用させたときは▽の代わりに grad という記号を使ってもよい。す なわち, ▽f=gradf. 後に述べるように, ▽をベクトルとみなしてベクトル関数に作用させ る(内積をとる)ときは, 記号 gradは使わない、ただし、式(1.13) の▽は grad を使って書 くことができる。

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TOEIC・英語 大学生・専門学校生・社会人

問5 英語の長文問題です選択式です! よろしくお願いします。

【問5】 次の Global Warming の段落を読んで、その下の英文 (S) が True (正 い) か False (誤り) のどちらか、選びなさい。 AM Global Warmind: All over the world people are talking about global warming. Vorld leaders are meeting to discuss this problem. Why is it such an important ISSU@? f the temperature of the earth rises too much, the polar ice CapS will begin to melt, causing the water level in the oceans to rise. The Intergovernmental Panel on Climate Change (the IPCC) has made Studies which suggest that there could be a one-meter rise in sea levels by the year 2080. No one knows exactly how bad the effect of this rise could be. However, it is thought that roughly 1 billion people who live on coastal land could experience severe impacts. The places most likely to be badly affected by this rise in sea level are tropical and warmer zoness: these are places where the coasts are more highly populated. The most vulnerable regions are located along the southern coast of the Mediterranean Sea, the west coast of Africa, and southern Asian countries like India, Sri Lanka, and Bangladesh. These regions contain some of the poorest, most heavily populated, and highly fertile areas of the world. In these areas, there will be huge problems as people's homes are flooded and qood farming land becomes useless. In the Pacific and Indian Oceans there are many island nations that will cease to exist. About 5 million people will have to move to other countries as the rising seas ruin drinking water and severe storms destroy their homes. The consequences of global warming will be devastating for billions of people. This is not only their problem, but an issue for the world to discuss. Much has to be done before the oceans come ashore. (S): Because of global warming, the temperature of ice and snoW IS increasin9. 〇 A. TRUE (〇) B. FALSE

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TOEIC・英語 大学生・専門学校生・社会人

問5 英語の長文問題です 選択式です よろしくお願いします。

【問5】 次の Global Warming の段落を読んで、その下の英文 (S) が True (正 い) か False (誤り) のどちらか、選びなさい。 AM Global Warmind: All over the world people are talking about global warming. Vorld leaders are meeting to discuss this problem. Why is it such an important ISSU@? f the temperature of the earth rises too much, the polar ice CapS will begin to melt, causing the water level in the oceans to rise. The Intergovernmental Panel on Climate Change (the IPCC) has made Studies which suggest that there could be a one-meter rise in sea levels by the year 2080. No one knows exactly how bad the effect of this rise could be. However, it is thought that roughly 1 billion people who live on coastal land could experience severe impacts. The places most likely to be badly affected by this rise in sea level are tropical and warmer zoness: these are places where the coasts are more highly populated. The most vulnerable regions are located along the southern coast of the Mediterranean Sea, the west coast of Africa, and southern Asian countries like India, Sri Lanka, and Bangladesh. These regions contain some of the poorest, most heavily populated, and highly fertile areas of the world. In these areas, there will be huge problems as people's homes are flooded and qood farming land becomes useless. In the Pacific and Indian Oceans there are many island nations that will cease to exist. About 5 million people will have to move to other countries as the rising seas ruin drinking water and severe storms destroy their homes. The consequences of global warming will be devastating for billions of people. This is not only their problem, but an issue for the world to discuss. Much has to be done before the oceans come ashore. (S): Because of global warming, the temperature of ice and snoW IS increasin9. 〇 A. TRUE (〇) B. FALSE

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TOEIC・英語 大学生・専門学校生・社会人

問3 英語の長文問題です 選択式です よろしくお願いします

【問3】 次の Global Warming の段落を読んで、その下の英文 (S) が い) か False (誤り) のどちらか、選びなさい。 (S) が True (正し Global Warming: All over the world people are talking about global warming. World leaders are meeting to discuss this problem. Why is it Such an Important ISSUG? If the temperature of the earth rises too much, the polar ice capS will begin to melt, causing the water level in the oceans to rise. The Intergovernmental Panel on Climate Change (the IPCC) has made studies which suggest that there could be a one-meter rise In Se levels by the year 2080. No one knows exactly how bad the effect of this rise could be. However, it is thought that roughly 1 billion people who live on coastal land could experience severe impacts. The places most likely to be badly affected by this rise in sea level are tropical and warmer ZoneS: these are places where the coasts are Ore highly populated. The most vulnerable regions are located along the southern coast of the Mediterranean Sea, the west coast of Africa, and southerm Asian countries like India, Sri Lanka, and Bangladesh. These regions contain some of the poorest, most heavily populated, and highly fertlle areaS of the world. In these areas, there will be huge problems as people's homes are flooded and good farming land becomes useless. In the Pacific and Indian Oceans there are many jsland nations that will cease to exist. About 5 million people will have to move to other countries as the rising seas ruin drinking water and severe storms destroy their homes. The consequences Of global warming will be devastatind for billions of people. This is not only their problem, but an ISSue for the world to discuss. Much has to be done before the oceans come aShore. (S): As a result of global warmin9, farms and fertile lands throughout the world will be destroyed. 〇 A_ TRUE () B.FALSE

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TOEIC・英語 大学生・専門学校生・社会人

問2 長文の英語です。 選択式です よろしくお願いします。

【問2】 次の Global Warming の段落を読んで、その下の英文 (S) が True (正 い) か False (誤り) のどちらか、選びなさい> Il間 Global Warming: All over the world people are talking about global warming. World leaders are meeting to discuss this problem. Why is it such an important ISSUG? If the temperature of the earth rises too much, the polar ice caps will begin to melt, causing the water level in the oceans to rise. The Intergovernmental Panel on Climate Change (the IPCC) has made studies which suggest that there could be a one-meter rise in sea levels by the year 2080. No one knows exactly how bad the effect of this rise could be. However, it is thought that roughly 1 billion people who live on coastal land could experience severe impacts. The places most likely to be badly affected by this rise in sea level are tropical and warmer zones: these are places where the coasts are more highly populated. The most vulnerable regions are located along the southern coast of the Mediterranean Sea, the west coast of Africa, and southern Asian countries like India, Sri Lanka, and Bangladesh. These reqions contain some of the poorest, most heavily populated, and hiqhly fertile areas of the world. In these areas, there will be huge problems as people's homes are flooded and good farming land becomes useless. In the Pacific and Indian Oceans there are many island nations that will cease to exist. About 5 million people will have to move to other countries as the rising seas ruin drinking water and severe storms destroy their homes. The consequences of global warming wlll be devastating for billions of people. This is not only their problem, but an issue for the world to discuss. Much has to be done before the oceans come ashore. (S): Rising sea-levels will decrease acceSsSs to clean drinking water for hundreds of millions of people. (〇 A_ TRUE (〇) B. FALSE

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TOEIC・英語 大学生・専門学校生・社会人

5問目 英語の長文問題です。 選択式です。よろしくお願いします。

【問5】 次の Global Warming の段落を読んで、その下の英文 (S) が True (正 い) か False (誤り) のどちらか、選びなさい。 AM Global Warmind: All over the world people are talking about global warming. Vorld leaders are meeting to discuss this problem. Why is it such an important ISSU@? f the temperature of the earth rises too much, the polar ice CapS will begin to melt, causing the water level in the oceans to rise. The Intergovernmental Panel on Climate Change (the IPCC) has made Studies which suggest that there could be a one-meter rise in sea levels by the year 2080. No one knows exactly how bad the effect of this rise could be. However, it is thought that roughly 1 billion people who live on coastal land could experience severe impacts. The places most likely to be badly affected by this rise in sea level are tropical and warmer zoness: these are places where the coasts are more highly populated. The most vulnerable regions are located along the southern coast of the Mediterranean Sea, the west coast of Africa, and southern Asian countries like India, Sri Lanka, and Bangladesh. These regions contain some of the poorest, most heavily populated, and highly fertile areas of the world. In these areas, there will be huge problems as people's homes are flooded and qood farming land becomes useless. In the Pacific and Indian Oceans there are many island nations that will cease to exist. About 5 million people will have to move to other countries as the rising seas ruin drinking water and severe storms destroy their homes. The consequences of global warming will be devastating for billions of people. This is not only their problem, but an issue for the world to discuss. Much has to be done before the oceans come ashore. (S): Because of global warming, the temperature of ice and snoW IS increasin9. 〇 A. TRUE (〇) B. FALSE

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TOEIC・英語 大学生・専門学校生・社会人

3問目 英語の長文問題 選択式です、よろしくお願いします。

【問3】 次の Global Warming の段落を読んで、その下の英文 (S) が い) か False (誤り) のどちらか、選びなさい。 (S) が True (正し Global Warming: All over the world people are talking about global warming. World leaders are meeting to discuss this problem. Why is it Such an Important ISSUG? If the temperature of the earth rises too much, the polar ice capS will begin to melt, causing the water level in the oceans to rise. The Intergovernmental Panel on Climate Change (the IPCC) has made studies which suggest that there could be a one-meter rise In Se levels by the year 2080. No one knows exactly how bad the effect of this rise could be. However, it is thought that roughly 1 billion people who live on coastal land could experience severe impacts. The places most likely to be badly affected by this rise in sea level are tropical and warmer ZoneS: these are places where the coasts are Ore highly populated. The most vulnerable regions are located along the southern coast of the Mediterranean Sea, the west coast of Africa, and southerm Asian countries like India, Sri Lanka, and Bangladesh. These regions contain some of the poorest, most heavily populated, and highly fertlle areaS of the world. In these areas, there will be huge problems as people's homes are flooded and good farming land becomes useless. In the Pacific and Indian Oceans there are many jsland nations that will cease to exist. About 5 million people will have to move to other countries as the rising seas ruin drinking water and severe storms destroy their homes. The consequences Of global warming will be devastatind for billions of people. This is not only their problem, but an ISSue for the world to discuss. Much has to be done before the oceans come aShore. (S): As a result of global warmin9, farms and fertile lands throughout the world will be destroyed. 〇 A_ TRUE () B.FALSE

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