流体力学课后作业1
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1.14For two 0.2-m-long rotating concentric cylinders, the velocity distribution is given by u (r ) = 0.4/r －l000r m/s. If the diameters of the cylinders are 2 cm and 4 cm, respectively , calculate the fluid viscosity if the torque on the inner cylinder is measured to be 0.0026 N·m.
解：已知：u (r ) = 0.4/r －l000r T=0.0026 N·m l=0.2m
又T=F ×R=τ·πdl ·r
对于极坐标而言，切应力表达式应为：
u u u r r r r r τμμ∂∂⎛⎫⎛⎫==- ⎪ ⎪∂∂⎝⎭⎝⎭
=μ（-0.4/r 2-1000-0.4/r 2+1000）
=-0.8μ/r 2，方向与速度方向相反。
推出：μ=Tr 2/（0.8πdl ·r ）=0.2586Pa ·s
1.20 A flow might reasonably be approximated as incompressible if the change of density with pressure at constant temperature is less than 0.5%.
a. What is the maximum pressure change possible for water to be considered
incompressible according to this criterion?
b. What is the maximum pressure change possible for air (initially at standard
sea-level conditions) to be considered incompressible according to this criterion?
解：a. 已知△ρ/ρ≤0.5% 求△P=?
αp ·△P=△ρ/ρ αp 外插至标准大气压（101325Pa ）下，得αp=0.54×10-9 有：△P=0.5%/（0.54×10-9）≈9.26MPa
b ．P=ρRT 当T 不变时 P/ρ=△P/△ρ
得.△P=P ·△ρ/ρ=101325×0.5%=507Pa