I have been staring at these two problems for a LONG time now and keep getting stuck. Please help me, and try to explain so I can understand.
ro = density
p = pressure
g = gravity
h = height/elevation
A = area
v = velocity
1a) Use the principal of dimensional consistency, show that bernoulli's equation written as:
P + (1/2)(ro)(v²) + (ro)gh = constant
has the dimension of pressure.
1b) When it is written as:
(ro)/[(ro)*g] + (v²)/(2g) + h = constant
show that each term has the dimension of length.
2) Using equations
a) A*v = A*v
Left side both have subscript 1, right side have subscript 2.
and the version of Bernoulli's equation:
P/(ro) + (v²)/2 + gh = constant
v(subscript 2) = sqrt((2*[p(sub1)-p(sub2)])/ (ro(1-[(A(sub2)/A(sub1))²])
Sorry if it's hard to read. I can't do this on my own and my roommate isn't here to tutor me like he usually does.
The Attempt at a Solution
I don't even understand 1a and 1b. For 2, I can get as far as
v[sub2] = [ro =(ro)gh - p]/[(ro)*(A(sub2)/A(sub1))²]
and that's just by creating similar denominators for the second equation and substituting for v[sub2] with what i solved for the other v in the other equation.