How Does Friction Affect Metal Flow in Sand Casting?

[Suitengu]

During pouring into a sand mold, the molten metal can be poured into the downsprue at a constant flow rate during the time it takes to fill the mold. At the end of pouring the sprue is filled and there is negligible metal in the pouring cup. The downsprue is 6 in. long. Its cross-sectional area at the top is 0.8 in^2 and the base is 0.6 in^2. The cross-sectional area leading from the sprue is also 0.6 in^2 and it is 8 in. long before leading into the mold cavity, whose volume is 65 in^3. The volume of the riser located along the runner near the mold cavity is 25 in^3. It takes a total of 3 sec to fill the entire mold. This is more than the theoretical time required, indicating a loss of velocity due to friction in the sprue and runner. Find

a)the theoretical velocity and flow rate at the base of the downsprue
b)the total volume of the mold
c)the actual velocity and flow rate at the base of the sprue and
d)the loss of head in the gating system due to friction

I guess my problem is i don't know how to calculate actual differently from theoretical as I only know one way to calculate which I am not even too sure of. Could someone give me a push to start off?

 

[Valkarie]

a) The theoretical velocity and flow rate at the base of the downsprue can be calculated using the Bernoulli equation. The Bernoulli equation states that the sum of the pressures, velocities, and potential (or gravitational) energies of a fluid must remain constant. Let P1 be the pressure at the top of the sprue, V1 be the velocity at the top of the sprue, and Z1 be the height of the top of the sprue above the base of the sprue. Let P2 be the pressure at the base of the sprue, V2 be the velocity at the base of the sprue, and Z2 be the height of the base of the sprue above the base of the sprue. The Bernoulli equation is then:P1 + ½*ρ*V1^2 + ρ*g*Z1 = P2 + ½*ρ*V2^2 + ρ*g*Z2where ρ is the density of the molten metal and g is the acceleration due to gravity. Assuming that the pressure at the top and base of the sprue are atmospheric, and the density of the molten metal is 8000 kg/m^3, the equation simplifies to:½*8000*V1^2 + 9.81*6 = ½*8000*V2^2 + 9.81*0Solving for V2 gives:V2 = 7.63 m/sThe flow rate at the base of the sprue can then be calculated by multiplying the velocity by the cross-sectional area of the sprue:Q = V2*A2 = 7.63*0.6 = 4.58 m^3/sb) The total volume of the mold is the volume of the cavity plus the volume of the riser. Vtotal = Vcavity + Vriser = 65 + 25 = 90 in^3c) The actual velocity and flow rate at the base of the sprue can be calculated using the energy equation. The energy equation states that the sum of the pressure, velocity, and friction losses in a pipe must remain constant. Let P1 be the pressure at the top of the sprue, V1 be the velocity at the top of

 

[piercas]

a) The theoretical velocity can be calculated using the Bernoulli's equation, which states that the velocity of a fluid is inversely proportional to the cross-sectional area of the pipe it is flowing through. The equation is as follows:

v = (2gh)^1/2

Where, v is the velocity, g is the acceleration due to gravity (9.8 m/s^2), and h is the height difference between the top and base of the downsprue.

In this case, h = 6 in. = 0.1524 m

Therefore, the theoretical velocity at the base of the downsprue is:

v = (2*9.8*0.1524)^1/2 = 1.38 m/s

The flow rate can be calculated by multiplying the velocity with the cross-sectional area of the downsprue at the base, which is 0.6 in^2 = 0.00387 m^2.

Therefore, the theoretical flow rate is:

Q = v*A = 1.38*0.00387 = 0.00534 m^3/s

b) The total volume of the mold can be calculated by adding the volume of the mold cavity (65 in^3 = 1.065*10^-4 m^3) and the volume of the riser (25 in^3 = 4.10*10^-5 m^3).

Therefore, the total volume of the mold is 1.475*10^-4 m^3.

c) The actual velocity and flow rate at the base of the downsprue can be calculated by taking into account the loss of velocity due to friction in the sprue and runner. This can be done by using the Darcy-Weisbach equation, which relates the head loss due to friction with the flow rate, pipe length, and pipe diameter. The equation is as follows:

hL = f (L/D)*v^2/2g

Where, hL is the head loss, f is the Darcy-Weisbach friction factor, L is the length of the pipe, D is the diameter of the pipe, v is the velocity, and g is the acceleration due to gravity.

Assuming a friction factor of 0.02 (typical for sand casting), the head loss in the downsprue can be calculated as:

h