化工传递作业题解1.docVIP

Reference answers of homework 1. What are the “orders” of the following quantities: 2) Write out the following summations: 4). Evaluate: 5). Verify: Evaluate: 7). Evaluate: 8). A field is said to be irrotational if . Which of the following fields are irrotational? b, c 9). Evaluate and for the four fields in exercise 8 0, b, 0, 0 2. 1) Please obtain , , and in any orthogonal curvilinear coordinates and their special forms in the three kinds of coordinates, rectangular, cylindrical and spherical coordinates. 2). If is the instantaneous position vector for a particle, show that the velocity and acceleration of the particle are given by: In cylindrical coordinate, the dots indicate time derivatives of the coordinates. Solution: 3. suppose we have a velocity profile Please find the track line and the stream line which pass when t=0 Solution: 1) stream line: C=1, so the stream line is 2) track line: from C1=1/2 from C2=1 4. Homework for you: Suppose there is a shear stress on the gas-liquid interface, , is a known value, please find the velocity profile for the cases when gas flows in cocurrent or countercurrent with liquid respectively. solution: boundary conditions (B.C.): (气体向上流动时取+号，向下流动时取-号) 将微分方程积分后： 可以定出： 当气体向下流动时， 当气体向上流动时， 5. Please find: 1)The relationship between and 2)Why , try to prove it 3)How to calibrate a flow meter with the relationship between Q and ? solution: 1) 2) from 3) 从 可知，两者为线性关系，不同流量下测定压力降，即可获得流量值。 6. Problems for you to consider as your homework: 1). Try to find a method to make the inner pipe without shear stress acting on it 2). How to make the shear stresses acting on inner and outer cylinders be equal? 如果使内筒以速度V0沿轴向运