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大气压力的变化

流体静力学的法律,p_a = \ρgh美元在一个给定的h美元。然而密度随高度和温度。温度不同的高度。g美元常数随高度。

如何表达大气压强的法律吗?

回答

>通过流体静力学的法律,p_a = \ρgh,美元在给定的h美元。然而密度随高度和温度。温度不同的高度。g常数随美元高度。表达式是水,这或多或少不变密度、深度而不是高度。Ynou需要改变这一个微分方程。这是相当简单的:$ $ \压裂{dP (h)} {dh} = - \ρg \标记{1}$ $这个假设大气流体静力学平衡:每层大气的熊的重量的所有质量高于层。另一个关键方程是理想气体定律,PV = nRT美元。这可以重写的当地密度$ $ P = \ρR_s T \标记{2}$ $ R_s美元是特定气体常数,理想气体常数除以平均分子质量的气体。结合方程(1)和(2)收益率$ $ \压裂{dP} {dh} = - \压裂{g} {R_s T} {3} $ $ P \标记假设g美元的所有因素,R_s,美元和T是常数导致美元指数:$ $ P (h) = P_0 \ exp \离开(- h \压裂{g} {R_s T} \右)= P_0 \ exp \离开(- \压裂{h} {h} \) \标记{4},P_0美元美元的压力在表面和h是美元比例因子的高度,h = R_s T / g美元。 The exponential atmosphere model assumes constant temperature. This is not a valid assumption. Temperature drops with increasing altitude in the troposphere, rises with increasing altitude in the stratosphere, and drops again with increasing altitude in the mesosphere. Above the mesosphere, the assumptions of a specific gas constant and constant gravitational acceleration also fail. The assumptions of a specific gas constant and constant gravitational acceleration are approximately valid in the troposphere. An approximate model for temperature in the troposphere is to assume a constant lapse rate $L$: $$T(h) = T_0 - L h\tag{5}$$ where $T_0$ is the temperature at the surface and $L$ is the lapse rate, the rate at which temperature decreases with altitude. Combining equations (3) and (5) results in a solvable first order differential equation, with solution $$P = P_0 \left(1-\frac{L}{T_0}h\right)^{\frac{g}{R_s L}}\tag{6}$$ This still assumes constant gravity and and constant atmospheric composition, and it assumes hydrostatic equilibrium (equation 1) and an ideal gas (equation 2). None of these are even approximately true above the mesosphere. Increasing accuracy means that atmosphere models become ever more empirical. The models are still tied to physics, but they are also tied to observations. Lower atmosphere weather models have to eliminate the assumptions that pressure, temperature, and atmospheric makeup are functions of elevation only. Upper atmosphere models have to account for variations in solar radiation. One solar flare can make the upper atmosphere expand by over an order of magnitude.

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