1. (40 points total) A metal container of height, H has an inside cross sectiona
ID: 1792670 • Letter: 1
Question
1. (40 points total) A metal container of height, H has an inside cross sectional weight of Wh When empty. The container is placed on a scale and water flows in through an opening at the top with a cross-sectional area, Ak (which is at an angle, 6, with respect to the horizontal line) and Figure 1 below. Under steady state conditions, the height of the water in the tank is h. The velocity at cross-sectional area labeled "2", i,, reaction force in the horizontal direction, and the reading on the scale are to be determined by answering the following. (Note:-Let density of water as p. Express all answers using smbolic parameters defined in the problem). out through two equal-area openings in the sides, Az and As as shown in (a) (7 points) Define a suitable control volume and a coordinate system for this analysis. Also indicate all relevantforcesacting on the control volume, + y 7 et -cy 2 b)(8 points) List all the relevant assumptions made for this analysis.Explanation / Answer
given
empty tank weight = Wtank
under steady state conditions
height of water = h
velocities form exits = v2, v3
entry velocity at angle theta = v1
a. control volume is teh whole volume of the tank as labelled
b. assumptions
steady state
constant density of water
uniform flow form the pipes
c. as in steady state the rate of change on volume oif water in the tank is zero
hence input volume rate = exit voplume rate
A1v1 = A2v2 + A3v3 ( from equation of continuity)
hence
v1 = (A2v2 + A3v3)/A1
d. for density rho of water
mass flow rate = rho*A*v
moemntum flux = mass flow rate * v
hence horizontal momentum flux = rho(A2v2^2 + A1v1^2*cos(theta) - A3v3^2)
e. vertical momentum flux = rho*A1*v1^2sin(theta)
f. reading on scale = W
W = Wtank + rho*g*h*Atank + rho*A1*v1^2sin(theta)
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