Question

2. (3 points) 2. Consider the following shock tube problem: $p_L = 1.0, \rho_L = 1.0, u_L = 0.0$ and $p_R = 0.04379, \rho_R = 0.1, u_R = 0.0$. Also, $\frac{p_2}{p_1} = 5.312$. Pressures are in bar and densities are in $kg/m^3$. All quantities are in non-dimensional units. a. Compute the induced velocity $u_p$ behind the shock. b. Use these values and for time $t = 0.05$ to calculate the location of the shock, the contact, and the tail and head of the expansion fan.

          2. (3 points) 2. Consider the following shock tube problem:
$p_L = 1.0, \rho_L = 1.0, u_L = 0.0$ and $p_R = 0.04379, \rho_R = 0.1, u_R = 0.0$. Also, $\frac{p_2}{p_1} = 5.312$. Pressures are in bar and densities are in $kg/m^3$.
All quantities are in non-dimensional units.
a. Compute the induced velocity $u_p$ behind the shock.
b. Use these values and for time $t = 0.05$ to calculate the location of the shock, the
contact, and the tail and head of the expansion fan.

2. (3 points) 2. Consider the following shock tube problem:
pL = 1.0, = 1.0, uL = 0.0 and pR = 0.04379, = 0.1, uR = 0.0. Also, (p2)/(p1) = 5.312. Pressures are in bar and densities are in kg/m^3.
All quantities are in non-dimensional units.
a. Compute the induced velocity up behind the shock.
b. Use these values and for time t = 0.05 to calculate the location of the shock, the
contact, and the tail and head of the expansion fan.

Added by Kristy G.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Adi S

10/18/2023

Step 1

The induced velocity behind the shock can be calculated using the Rankine-Hugoniot jump conditions for a shock wave: u_p = (p_R - p_L) / (ρ_R * (1 / ρ_L - 1 / ρ_R)) Where: p_R = 0.04379 p_L = 1.0 ρ_R = 0.1 ρ_L = 1.0 Substitute the given values into the Show more…

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(3 points) 2. Consider the following shock tube problem: p_(L)=1.0, ho _(L)=1.0,u_(L)=0.0 and p_(R)=0.04379, ho _(R)=0.1,u_(R)=0.0. Also, (p_(2))/(p_(1))= 5.312. Pressures are in bar and densities are in k(g)/(m^(3)). All quantities are in non-dimensional units. a. Compute the induced velocity u_(p) behind the shock. b. Use these values and for time t=0.05 to calculate the location of the shock, the contact, and the tail and head of the expansion fan. 2. (3 points) 2. Consider the following shock tube problem: PL = 1.0,PL =1.0,uL = 0.0 and pR = 0.04379,PR = 0.1,uR = 0.0. Also, Pz 5.312. Pressures are in bar and densities are in kg/m3. All quantities are in non-dimensional units a. Compute the induced velocity un behind the shock b. Use these values and for time t = 0.05 to calculate the location of the shock, the contact, and the tail and head of the expansion fan Ror1