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Suppose that a liquid has an appreciable compressibility. Its density therefore varies with depth and pressure....
Suppose that a liquid has an appreciable compresibility. Its density therefore varies with depth and pressure....
Suppose that a liquid has an appreciable compresibility. Its density therefore varies with depth and pressure. The density at the surface is ρ0 Show that the density varies with pressure according to ρ=ρoekp (Where p is gauge pressure at any depth, and k is the compressibillity.) Find p as a function of depth, y.
Q1 20 points. Two tanks contain liquid filled to the same depth h as shown below Liquid A: Has a constant density p...
Q1 20 points. Two tanks contain liquid filled to the same depth h as shown below Liquid A: Has a constant density pAPo Liquid B: The density varies with position acording to the formula pn() where the coordinate z is shown in the figure. 0 is the bottom of each tank while z = h is the top of the liquid surface exposed to atmosphere. The : liquids are in hydrostatic equilibrium. Two tanks containing liquids with the same depth...
1. Consider the volume of a substance as a function of pressure and temperature. Use the...
1. Consider the volume of a substance as a function of pressure and temperature. Use the Euler chain relation and the definitions of the thermal expansivity and the isothermal compressibility to show that др ) - a LOT J KT is true. 2. At 363 K and 1 bar, liquid toluene has a thermal expansivity of 1.284 x 10'K' and an isothermal compressibility of 1.972 x 10 bar. Suppose a rigid container is completely filled with liquid toluene at 362.5...
Consider the steady, incompressible flow of depth h of a liquid of known density ρ and...
Consider the steady, incompressible flow of depth h of a liquid
of known density ρ and unknown viscosity µ down a flat plate as
shown in Figure 1. Air is the fluid above the liquid layer. The
force of gravity is in the vertical direction with acceleration g,
and the plate is at an angle θ with respect to the horizontal.
Assuming the coordinate system as shown, with x aligned with the
flow direction, and y normal to the plate,...
A cyclindrical container filled with a liquid of density p rotates about an axis through its...
A cyclindrical container filled with a liquid of density p rotates about an axis through its center with an angular velocity w. A Cartesian coordinate system in standard orientation is introduced with its origin at the lowest point on the fluid surface. The pressure above the liquid surface is P_0. (a) Notice that a thin imaginary tube with cross-section area A lies along the -axis. Draw a free boy diagram for a slice of liquid within this tube, lying between...
40. The atmospheric pressure (force per unit area) on a surface at an altitude z is due to the we...
problem 40 with parts
40. The atmospheric pressure (force per unit area) on a surface at an altitude z is due to the weight of the column of air situated above the surface. Therefore, the difference in air pressure p between the top and bottom of a cylindrical volume element of height Az and cross-section area A equals the weight of the air enclosed (density ρ times volume V-: ΑΔε times gravity g), per unit area: Let Δ、→0 to derive...
The boiling temperature of nitrogen at atmospheric pressure at sea level (1 atm pressure) is -196°C. Therefore, nitroge...
The boiling temperature of nitrogen at atmospheric pressure at sea level (1 atm pressure) is -196°C. Therefore, nitrogen is commonly used in low-temperature scientific studies since the temperature of liquid nitrogen in a tank open to the atmosphere will remain constant at -196°C until it is depleted. Any heat transfer to the tank will result in the evaporation of some liquid nitrogen, which has a heat of vaporization of 198 kJ/kg and a density of 810 kg/m3 at 1 atm....
Q.4 (22') Suppose the joint probability density function of X and Y is fx,y(x, y) =...
Q.4 (22') Suppose the joint probability density function of X and Y is fx,y(x, y) = { „) - k(2 - x + y)x 0 sxs 1,0 sys1 o otherwise (a) (7”) Show that the value of constant k = 12 (b) (7') Find the marginal density function of X, i.e., fx(x). (c) (8') Find the conditional probability density of X given Y=y, i.e., fxy(xly). 11
Suppose the random variable X has probability density function (pdf) - { -1 < x<1 otherwise...
Suppose the random variable X has probability density function (pdf) - { -1 < x<1 otherwise C fx (x) C0 : where c is a constant. (a) Show that c = 1/7; (b) Graph fx (х); (c) Given that all of the moments exist, why are all the odd moments of X zero? (d) What is the median of the distribution of X? (e) Find E (X2) and hence var X; (f) Let X1, fx (x) What is the limiting...
Show the steps. Thank you 9. An isolated spherical spherical capacitor has charge +Q on its...
Show the steps. Thank you
9. An isolated spherical spherical capacitor has charge +Q on its inner conductor (radius ra) and charge-Q on is outer conductor (radius rb). Half of the volume between the conductors is then filled with a liquid dielectric of constant K. Given [ra, Tb, Q, K] Determine: a. the capacitance of the half filled capacitor. b. The Electric Field in the volume between the two conductors as a function of distance r from the center of...
Q1 20 points. Two tanks contain liquid filled to the same depth h as shown below Liquid A: Has a constant density pAPo Liquid B: The density varies with position acording to the formula pn() where the coordinate z is shown in the figure. 0 is the bottom of each tank while z = h is the top of the liquid surface exposed to atmosphere. The : liquids are in hydrostatic equilibrium. Two tanks containing liquids with the same depth...
1. Consider the volume of a substance as a function of pressure and temperature. Use the Euler chain relation and the definitions of the thermal expansivity and the isothermal compressibility to show that др ) - a LOT J KT is true. 2. At 363 K and 1 bar, liquid toluene has a thermal expansivity of 1.284 x 10'K' and an isothermal compressibility of 1.972 x 10 bar. Suppose a rigid container is completely filled with liquid toluene at 362.5...
Consider the steady, incompressible flow of depth h of a liquid
of known density ρ and unknown viscosity µ down a flat plate as
shown in Figure 1. Air is the fluid above the liquid layer. The
force of gravity is in the vertical direction with acceleration g,
and the plate is at an angle θ with respect to the horizontal.
Assuming the coordinate system as shown, with x aligned with the
flow direction, and y normal to the plate,...
problem 40 with parts
40. The atmospheric pressure (force per unit area) on a surface at an altitude z is due to the weight of the column of air situated above the surface. Therefore, the difference in air pressure p between the top and bottom of a cylindrical volume element of height Az and cross-section area A equals the weight of the air enclosed (density ρ times volume V-: ΑΔε times gravity g), per unit area: Let Δ、→0 to derive...
The boiling temperature of nitrogen at atmospheric pressure at sea level (1 atm pressure) is -196°C. Therefore, nitrogen is commonly used in low-temperature scientific studies since the temperature of liquid nitrogen in a tank open to the atmosphere will remain constant at -196°C until it is depleted. Any heat transfer to the tank will result in the evaporation of some liquid nitrogen, which has a heat of vaporization of 198 kJ/kg and a density of 810 kg/m3 at 1 atm....
Q.4 (22') Suppose the joint probability density function of X and Y is fx,y(x, y) = { „) - k(2 - x + y)x 0 sxs 1,0 sys1 o otherwise (a) (7”) Show that the value of constant k = 12 (b) (7') Find the marginal density function of X, i.e., fx(x). (c) (8') Find the conditional probability density of X given Y=y, i.e., fxy(xly). 11
Suppose the random variable X has probability density function (pdf) - { -1 < x<1 otherwise C fx (x) C0 : where c is a constant. (a) Show that c = 1/7; (b) Graph fx (х); (c) Given that all of the moments exist, why are all the odd moments of X zero? (d) What is the median of the distribution of X? (e) Find E (X2) and hence var X; (f) Let X1, fx (x) What is the limiting...
Show the steps. Thank you
9. An isolated spherical spherical capacitor has charge +Q on its inner conductor (radius ra) and charge-Q on is outer conductor (radius rb). Half of the volume between the conductors is then filled with a liquid dielectric of constant K. Given [ra, Tb, Q, K] Determine: a. the capacitance of the half filled capacitor. b. The Electric Field in the volume between the two conductors as a function of distance r from the center of...
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