溶液从高 [tex=2.571x1.214]dXGVQhFDAMonyA56CIMeKzio/EWDYc+r8pkJ3fp1CtQ=[/tex]顶圆直径[tex=2.286x1.0]i/n/jbBPwXz/FPZ6foTn9gHMuTcg8DdIJCxuptJrIXI=[/tex]的正圆锥形漏斗中漏入一直径为 [tex=2.286x1.0]+vaERUYGAkTrjzp1H5gjwf9Bt3cMZtVo6pe7A4aAQng=[/tex] 的圆柱形筒中. 开始时漏斗中盛满了溶液. 已知当溶液在漏斗中高为[tex=2.286x1.0]i/n/jbBPwXz/FPZ6foTn9gHMuTcg8DdIJCxuptJrIXI=[/tex]时，其表面下降的速度为[tex=4.286x1.357]1J6qnixJv0uYE10p8dTv+cIMtS+O7amKz15OBONiOhg=[/tex]问此时圆柱形筒中溶液表面上升的速率为多少?

2022-07-26

溶液从高 [tex=2.571x1.214]dXGVQhFDAMonyA56CIMeKzio/EWDYc+r8pkJ3fp1CtQ=[/tex]顶圆直径[tex=2.286x1.0]i/n/jbBPwXz/FPZ6foTn9gHMuTcg8DdIJCxuptJrIXI=[/tex]的正圆锥形漏斗中漏入一直径为 [tex=2.286x1.0]+vaERUYGAkTrjzp1H5gjwf9Bt3cMZtVo6pe7A4aAQng=[/tex] 的圆柱形筒中. 开始时漏斗中盛满了溶液. 已知当溶液在漏斗中高为[tex=2.286x1.0]i/n/jbBPwXz/FPZ6foTn9gHMuTcg8DdIJCxuptJrIXI=[/tex]时，其表面下降的速度为[tex=4.286x1.357]1J6qnixJv0uYE10p8dTv+cIMtS+O7amKz15OBONiOhg=[/tex]问此时圆柱形筒中溶液表面上升的速率为多少?

答案：

设[tex=0.429x0.929]gQzDwVIykgengUJAyMAHkQ==[/tex]时刻圆锥形漏斗中液面高度为[tex=0.857x1.214]yFaEBpOGQtieE/dHlY7yCw==[/tex]液面圆半径为 [tex=0.786x1.0]8oOcqqj8I2sD1c9gKsiFhQ==[/tex]由題意知[tex=4.571x2.429]AM8r23NOOtZ4AIpw1mZtNWbUn6OpD0pkRHp+pEXVFfGdpOvdeJ5tpxl6sYuubW3m[/tex]即[tex=4.214x2.357]vsg1EoU3oBSt/OtUJqnA9iKMyD1mmqfm5kGJrJX+cGM=[/tex]又设[tex=0.429x0.929]gQzDwVIykgengUJAyMAHkQ==[/tex]时刻圆柱形筒中液面高度为[tex=1.143x1.214]NLXRTYpB7qUblTNVAvJiDw==[/tex]据题意知圆柱形筒内溶液体积为              [tex=24.714x2.5]0iDURHKVkzej+QyrcT7yKvGtlBHQI8BbtNnWtvmK2P2JIPpqsEYB5VeXHdXKuzgjsJWpgevHVbPJorMvcyVlaN95qTsFawR+dgmLH09que0LMYuerh1mFD10OHnDzyGvgkgQh75wkxf3UsFANdQ2Uj7iiUNaiDZ56WF35enyCvC+Gl9I4exYrGK7AVC5TZDWti4DV8A72sAvjrfsdK4hDSMqzjH3zHDOWW7ErbK/ylLrWV5YzDj44nhCLNH+AWRB[/tex]上式两边对[tex=0.429x0.929]gQzDwVIykgengUJAyMAHkQ==[/tex]求导，有 [tex=9.071x2.429]MUI+Uao0KLn5mnJAVaCdxW+i+jfIGNSptjLvV/+UogtIl/Nc8KAoWB93D/aRCD/ri7ijpVQ7xYZi3k+jCbIfZmPCCc2FWP1vMXuVfFiN6G/YYwM1P1GlZVuY7EqPdRLtwceI7hA3/w8C/5uFS3TjLQ==[/tex]当 [tex=2.357x1.0]691lFFjMGkOaUsyWKZtvTw==[/tex] 时[tex=4.071x2.429]o5UGDRgLeUoLzD6FvhvL8wFVeZSO/7nHTHpltpn/LxIdf57NiYH0gxwWsRfFGdKU[/tex]代入上式，得[tex=12.214x2.429]UDOJYaodf9XT86FEQ7X4gpp2+lkyL6/LPIXB2W5I7nzq/lYgfdPL5sJWfb8+cY+zUF7h+6okOiwLIHMUCdoREhcq9hZffooz/4S2EqeY5Yc20YujkFLPmugGhW9SC68c[/tex]即圆柱形筒中溶液表面上升速率为[tex=5.5x1.357]1yA6+D7ALMsOzSTFW6ZFm/wtXTI9yUkrVRQZtgBPhdIoRyGBY77FZha5j0LnUFnt[/tex]

举一反三

内容

0
设[tex=0.857x1.0]N7iCrOsS+NNEUUlnsYCi1g==[/tex]服从参数为 1 的指数分布,[tex=2.286x1.0]9/9iwGqXp5QMYqkNTltYDNEowzysbRa2vywE4TxIMeI=[/tex],求[tex=2.214x1.357]ocoZdV18P73QTNWKFIScyg==[/tex].
1
set1 = {x for x in range(10)} print(set1) 以上代码的运行结果为？ A: {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} B: {0, 1, 2, 3, 4, 5, 6, 7, 8, 9,10} C: {1, 2, 3, 4, 5, 6, 7, 8, 9} D: {1, 2, 3, 4, 5, 6, 7, 8, 9,10}
2
[tex=3.143x1.286]BKrsxVq4bENQKOMraHT6YKvgKxRD4z8tM4Uy065DU4I=[/tex]溶液中滴加 [tex=2.286x1.0]w0rPP/A7t2v4C0apJ5BXSA==[/tex] 溶液时，先生成白色沉淀，而后溶解，再加入[tex=2.286x1.0]5612EONE3x+kbGb++mhxyg==[/tex] 溶液时并无沉淀生成，但加入少许 [tex=2.214x1.214]mlUO0KiaWyEaLhJl/oKn4WWDVI2RKgoD+tE3vz5Ybgw=[/tex] 溶液时就析出黑色沉淀。
3
电池[tex=20.143x1.571]QRfRQkTJBgxsqqWfwLVGcm1BPS4ktV2ytoUFQan+6l05TdKC5o+ckXnZ86SDv6Xvv5Ld5XKJvoQOP7b6wzroCJu0f9wBaH0PRbWmRXDOcLxYabFot++aP7PS1ZViq7o/b+J/H55Ey7QPiJh0jmy7hqchwGWSYmYmnA/jvr6gqRFFtvsw19seAFirolSf/VF3Z1PhN5r9+VD+moCAKY9mNw==[/tex]在 [tex=2.286x1.0]mQC5bVhEvIohRXFWIzFj6DUFZ1YD0n5SRbSxduotRAY=[/tex] 时的电动势为 [tex=3.571x1.0]V2zUDU4Z5Jx/AfRlpl8VlF15mVlcNpdIs0FIqoS2NjE=[/tex] 。计算 [tex=2.571x1.214]Jj3tTb8y/A0I1bhIpu9H8pNl+2TdGWsPD4gV4HI1NPM=[/tex]在该溶液中的平均活度因子。
4
[tex=10.214x1.429]/LTB/AKdzlj8A5bn0ikx64AaMQRo5QvWeHLkJzt7XZK6bKqjQkqV0RZl4M50xcWVY7xzfhw7QzXQNvf+RuGEwOOE7Imvp8GXaEqGoj2it6A=[/tex] 溶液 [tex=3.214x1.214]tyv2Uulj+W/3xzUcdofi+bLwGXUrzanCwS7FHlgcjYA=[/tex] 和 [tex=10.214x1.429]seHyLpay1Zeo0ib4E0psSFszZFWcwcKV78mdPEUOIU251mUgBb2bhaVatVYEt0HAEMzI6eLy1i3FuWp2bM0JPc0b5MZjNKJRC3k2iJ5/tlw=[/tex]溶液 [tex=2.714x1.214]EkUqh6uka2JeFCyqSCKH4eC7MtJa1OPVwAodME1/1/k=[/tex]混合后，溶液的 [tex=1.357x1.214]5Y4aY4NNGp2CUHfWC5RWGA==[/tex]为多少？若向溶液中加入 [tex=8.786x1.214]eSf8en7mCJGTZyWvUasj2WX8tAKQwoIr7hTthI5heymMeMy22Fkc94HT1XgpaKPdVWXscOsIivH5t6YSsjQ0ow==[/tex]溶液 [tex=3.0x1.429]6QcOcBU6ciX1XIkv8i3l+Y70mWOixBBYQsIvvdH4OqY=[/tex]溶液的 [tex=1.357x1.214]5Y4aY4NNGp2CUHfWC5RWGA==[/tex]为多少 ?