由假设得到公式 1. We assume laminar flow and use bernoulli’ equation:(由假设得到的公式) 公式 Where 符号解释 According to the assumptions, at every junction we have(由于假设) 公式 由原因得到公式 2. Because our field is flat we have AI so the height of our source relative to our sprinklers does not affect the exit speed v2(由原因得到的公式) 公式 Since the fluid is incompressible(由于液体是不可压缩的), we have Where 式式 用原来的公式推出公式 3. Plugging vI into the equation for v2, we obtain(将公式1代入公式2中得到) 公式 1l. Putting these together((把公式放在一起), because of the law of conservation of energy ields 公式 12. Therefore,from(2)(3)5), we have the ith junction(由前几个公式得) 公式 Putting(1)-(5)together, we can obtain pup at every junction. in fact, at the last junction, we have 公式 Putting these into(1), we get(把这些公式代入1中) 公式 Which means that the ly, h is about From these equations,(从这个公式中我们知道) we know that. 引出约束条件 4. Using pressure and discharge data from Rain Bird Gi/R, We find the attenuation factor(得到衰减因子,常数,系数)tobe 公式 计算结果 6. To find the new pressure, we use the(00), which states that the volume of water flowing in equals the volume of water flowing out:(为了找到新值,我们用什么方程) 八 式 Where Ois 7. Solving for vn we obtain(公式的解) 公式 Where n is the
由假设得到公式 1．We assume laminar flow and use Bernoulli’s equation:（由假设得到的公式） 公式 Where 符号解释 According to the assumptions, at every junction we have （由于假设） 公式 由原因得到公式 2．Because our field is flat, we have 公式, so the height of our source relative to our sprinklers does not affect the exit speed v2 （由原因得到的公式）； 公式 Since the fluid is incompressible(由于液体是不可压缩的), we have 公式 Where 公式 用原来的公式推出公式 3．Plugging v1 into the equation for v2 ,we obtain （将公式 1 代入公式 2 中得到） 公式 11．Putting these together(把公式放在一起), because of the law of conservation of energy, yields： 公式 12．Therefore, from (2),(3),(5), we have the ith junction（由前几个公式得） 公式 Putting (1)-(5) together, we can obtain pup at every junction . in fact, at the last junction, we have 公式 Putting these into (1) ,we get（把这些公式代入 1 中） 公式 Which means that the Commonly, h is about From these equations, （从这个公式中我们知道）we know that ……… 引出约束条件 4．Using pressure and discharge data from Rain Bird 结果, We find the attenuation factor （得到衰减因子，常数，系数） to be 公式 计算结果 6．To find the new pressure ,we use the ( 0 0),which states that the volume of water flowing in equals the volume of water flowing out : （为了找到新值，我们用什么方程） 公式 Where () is ;; 7．Solving for VN we obtain (公式的解) 公式 Where n is the …
8. We have the following differential equations for speeds in the x- and y-directions 公式 Whose solutions are (#f) 公式 9. We use the following initial conditions(使用初值) to determine the drag constant: 公式 根据原有公式 10. We apply the law of conservation of energy(根据能量守恒定律). The work done by the fc 公式 The decrease in potential energy is(势能的减少) 式 he increase in kinetic energy is(动能的增加) 式 Drug acts directly against velocity, so the acceleration vector from drag can be found Newtons awF=maas:(牛顿第二定律) Where a is the acceleration vector and m is mass Using the Newtons Second Law, we have that F/m=a and 公式 公式 Setting the two expressions for tI/t2 equal and cross-multiplying gives 公式 22. We approximate the binomial distribution of contenders with a normal distribution 公式 Where x is the cumulative distribution function of the standard normal distribution. Clearing denominators and solving the resulting quadratic in b gives 公式 As an analytic approximation to for k=l, we get B=c 26. Integrating,(使结合) we get PVT= constant,. where The main composition of the air is nitrogen and oxygen, so i=5 and r=1. 4, so 23. According to First Law of Thermodynamics, we get 公式 Where( ) we also then have Where P is the pressure of the gas and v:公式 V is the volume We put them into the Ideal gas Internal Formula: 公式 Where
8．We have the following differential equations for speeds in the x- and y- directions: 公式 Whose solutions are （解） 公式 9．We use the following initial conditions ( 使用初值 ) to determine the drag constant: 公式 根据原有公式 10．We apply the law of conservation of energy（根据能量守恒定律）. The work done by the forces is 公式 The decrease in potential energy is （势能的减少） 公式 The increase in kinetic energy is (动能的增加) 公式 Drug acts directly against velocity, so the acceleration vector from drag can be found Newton’s law F=ma as : (牛顿第二定律) Where a is the acceleration vector and m is mass Using the Newton’s Second Law, we have that F/m=a and 公式 So that 公式 Setting the two expressions for t1/t2 equal and cross-multiplying gives 公式 22．We approximate the binomial distribution of contenders with a normal distribution: 公式 Where x is the cumulative distribution function of the standard normal distribution. Clearing denominators and solving the resulting quadratic in B gives 公式 As an analytic approximation to . for k=1, we get B=c 26．Integrating, （使结合）we get PVT=constant, where 公式 The main composition of the air is nitrogen and oxygen, so i=5 and r=1.4, so 23．According to First Law of Thermodynamics, we get 公式 Where ( ) . we also then have 公式 Where P is the pressure of the gas and V is the volume. We put them into the Ideal Gas Internal Formula: 公式 Where
对公式变形 13. Define a= nlw to be the()(定义); rearranging(1) produces(将公式变形得到) 公式 We maximize E for each layer, subject to the constraint(2). The calculations are easier if we minimize 1/E.(为了得到最大值,求他倒数的最小值) Neglecting constant factors(忽略常 数), we minimize 公式 使服从约束条件 14. Subject to the constraint(使服从约束条件) 公式 Where B is constant defined in(2). However, as long as we are obeying this constraint, we can write(根据约束条件我们得到) 公式 And thus f depends only on h, the function f is minimized at(求最小值) 公式 At this value of h the constraint reduces to 公式 结果说明 15. This implies (HA) that the harmonic mean of l and w should be 公式 5. This value shows very little loss due to friction.(结果说明) The escape speed with friction is 公式 16. We use a similar process to find the position of the droplet, resulting in 公式 With t=00001 s, error from the approximation is virtually zero 17. We calculated its trajectory(轨道) using 公式 18. For that case, using the same expansion for e as above 公式 19. Solving for t and equating it to the earlier expression for t, we get 公式 20. Recalling that in this equality only n is a function of f, we substitute for n and solve for f. the result is 公式 Asv=., this equation becomes singular(单数的 由语句得到公式 21. The revenue generated by the flight is 公式 24. Then we have
对公式变形 13．Define A=nlw to be the ( )（定义）; rearranging (1) produces （将公式变形得到） 公式 We maximize E for each layer, subject to the constraint (2). The calculations are easier if we minimize 1/E.（为了得到最大值，求他倒数的最小值） Neglecting constant factors （忽略常 数）, we minimize 公式 使服从约束条件 14．Subject to the constraint （使服从约束条件） 公式 Where B is constant defined in (2). However, as long as we are obeying this constraint, we can write （根据约束条件我们得到） 公式 And thus f depends only on h , the function f is minimized at （求最小值） 公式 At this value of h, the constraint reduces to 公式 结果说明 15．This implies（暗示） that the harmonic mean of l and w should be 公式 So , in the optimal situation. ……… 5．This value shows very little loss due to friction.（结果说明） The escape speed with friction is 公式 16． We use a similar process to find the position of the droplet, resulting in 公式 With t=0.0001 s, error from the approximation is virtually zero. 17．We calculated its trajectory(轨道) using 公式 18．For that case, using the same expansion for e as above, 公式 19．Solving for t and equating it to the earlier expression for t, we get 公式 20．Recalling that in this equality only n is a function of f, we substitute for n and solve for f. the result is 公式 As v=…, this equation becomes singular (单数的). 由语句得到公式 21．The revenue generated by the flight is 公式 24．Then we have
公式 We differentiate the ideal-gas state equation 式 公式 25. We eliminate dT from the last two equations to get(排除因素得到) 公式 22. We fist examine the path that the motorcycle follows. Taking the air resistance into account differential 公式 Where P is the relative pressure We must first find the speed vl of water at our source: (*3J) 式
公式 We differentiate the ideal-gas state equation 公式 Getting 公式 25．We eliminate dT from the last two equations to get （排除因素得到） 公式 22．We fist examine the path that the motorcycle follows. Taking the air resistance into account, we get two differential equations 公式 Where P is the relative pressure. We must first find the speed v1 of water at our source: （找初值） 公式