Question

a) Show that a mass of fluid is at rest under the
forces
X =(y+z) - x
Y = (z+x)" - y
Z=(x + y)² - 2
and x² + y2 +22 – 2yż– 2zx - 2xy = constant are
the equations of the equi-pressure surfaces.
4+4​

Answer 1

Step-by-step explanation:

Let's solve for x.

x=y+z−x

Step 1: Add x to both sides.

x+x=−x+y+z+x

2x=y+z

Step 2: Divide both sides by 2.

2x/2=y+z/2

x=1/2y+

1/2z

Answer:

x=1/2y+1/2z

Let's solve for x.

y=z+x−y

Step 1: Flip the equation.

x−y+z=y

Step 2: Add y to both sides.

x−y+z+y=y+y

x+z=2y

Step 3: Add -z to both sides.

x+z+−z=2y+−z

x=2y−z

Answer:

x=2y−z

z=(x+y)2−2

Distribute:

z=x2+2xy+y2+−2

Answer:

z=x2+2xy+y2−2

Let's simplify step-by-step.

x2+y2+22−2yz−2zx−2xy

=x2+y2+22+−2yz+−2xz+−2xy

Answer:

=x2−2xy−2xz+y2−2yz+22