The velocity field of a 2-D flow on x-y plane is u = -x + y, v=x+y, d) Determine the angular deformation rate of the x - y plane. e) Determine the normal strain rate of the x and y axes, respectively. f) If the flow is inviscid, determine if Bernoulli's equation is applicable to the entire flow field. g) If the flow is inviscid, the fluid density is p, the static pressure at (x = 0, y = 0) is p= Po, and the gravitational field is ignored (say the flow field is on a space station), determine the pressure field based on the Bernoulli's equation. h) Starting from Newton's 2nd law for a fluid element, write down the differential equations for a fluid element in the flow field specified in g). Derive the pressure distribution in the flow field by using the boundary condition at (x = 0, y = 0), and compare the result with that of g). They should be consistent. (hint: solving partial differential equations the constant coming out of the integration may depend on other independent variables, just like what happened in solving stream line functions or pressure fields)
The velocity field of a 2-D flow on x-y plane is u = -x + y, v=x+y, d) Determine the angular deformation rate of the x - y plane. e) Determine the normal strain rate of the x and y axes, respectively. f) If the flow is inviscid, determine if Bernoulli's equation is applicable to the entire flow field. g) If the flow is inviscid, the fluid density is p, the static pressure at (x = 0, y = 0) is p= Po, and the gravitational field is ignored (say the flow field is on a space station), determine the pressure field based on the Bernoulli's equation. h) Starting from Newton's 2nd law for a fluid element, write down the differential equations for a fluid element in the flow field specified in g). Derive the pressure distribution in the flow field by using the boundary condition at (x = 0, y = 0), and compare the result with that of g). They should be consistent. (hint: solving partial differential equations the constant coming out of the integration may depend on other independent variables, just like what happened in solving stream line functions or pressure fields)
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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The velocity field of a 2-D flow on x-y plane is u = -x + y, v=x+y,
d) Determine the angular deformation rate of the x - y plane.
e) Determine the normal strain rate of the x and y axes, respectively.
f) If the flow is inviscid, determine if Bernoulli's equation is applicable to the entire flow field.
g) If the flow is inviscid, the fluid density is p, the static pressure at (x = 0, y = 0) is p= Po, and the gravitational field is ignored (say the flow field is on a space station), determine the pressure field based on the Bernoulli's equation.
h) Starting from Newton's 2nd law for a fluid element, write down the differential equations for a fluid element in the flow field specified in g). Derive the pressure distribution in the flow field by using the boundary condition at (x = 0, y = 0), and compare the result with that of g). They should be consistent. (hint: solving partial differential equations the constant coming out of the integration may depend on other independent variables, just like what happened in solving stream line functions or pressure fields)
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