Find the dimensions (in terms of mass (M), length (L), and time (T)) of the following; you may choose any length unit, time unit, and mass unit in S.I system. Use the definition of Force from Newton's second law of motion.
K_(1)=sigma sqrt{pi a}; where sigma is stress and a is crack length; pi is a dimensionless number
What is the unit and dimension of K_(1)? Note: stress is defined as force/area.
q=kA(d heta)/(dx); where q is heat flow in Watts; A is area; heta is temperature and x is distance
What is the unit and dimension of "k"? Note that "d" stands for derivative.
Re=(
ho ux)/(mu); where p is density, u is speed; x is characteristic length; and mu is viscosity as given by kg/(meter*sec).
What is the unit and dimension of "Re"?
Lift=(1/2)C_(l)
ho v^(2)A;
ho is air density, v is the air speed, A is area of the platform and C_(l) is a number (lift coefficient).
What is the unit and dimension of Lift?
omega=(cv)/(r^(2)); omega is angular velocity; v is linear velocity; r is the radius.
What is the dimension of 'c' if the equation is to be consistent
Find the dimensions (in terms of mass (M), length (L), and time (T)) of the following; you may choose any law of motion. Length unit, time unit, and mass unit in S.I system. Use the definition of Force from Newton's second
1) K= oVna; where o is stress and a is crack length; n is a dimensionless number
What is the unit and dimension of Kt? Note: stress is defined as force/area.
2) q=kA; where q is heat flow in Watts; A is area; O is temperature and x is distance dx
What is the unit and dimension of "k"? Note that "d" stands for derivative.
3) Re=(
ho ux)/(mu); where p is density, u is speed; x is characteristic length; and mu is viscosity as given by kg/(meter*sec).
What is the unit and dimension of "Re"?
4) Lift= CPv^(2)A; p is air density, v is the air speed, A is area of the platform and C is a number (lift coefficient).
What is the unit and dimension of Lift?
5) CV; w is angular velocity; v is linear velocity; r is the radius.
What is the dimension of 'c' if the equation is to be consistent
