Problem 5. The height of a horizontal channel is y = 1/x, for 1 < x < 2, where x = 1 is the entr

a) To compute the inlet mass flow rate per unit depth of the channel, we need to find the volume

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Problem 5. The height of a horizontal channel is y = 1/x, for 1 < x < 2, where x = 1 is the entrance and x = 2 the exit. Water flows into the channel with velocity u_in = 2, as shown in the figure, where solid lines indicate the channel walls. The flow is in steady state. Assume that the flow is 1-D and u is uniform on each cross-section area. a) If the fluid density is rho = 1000, compute the inlet mass flow rate per unit depth of the channel. i.e. the depth of the channel in z-direction W = 1. b) Derive the flow velocity, u, as a function of x. c) If the ambient pressure is uniform (1 atm), compute the force to anchor the channel on the ground (again, for unit width of channel, W = 1). Be careful with the sign.

          Problem 5. The height of a horizontal channel is y = 1/x, for 1 < x < 2, where x = 1 is the entrance and x = 2 the exit. Water flows into the channel with velocity u_in = 2, as shown in the figure, where solid lines indicate the channel walls. The flow is in steady state. Assume that the flow is 1-D and u is uniform on each cross-section area.

a) If the fluid density is rho = 1000, compute the inlet mass flow rate per unit depth of the channel. i.e. the depth of the channel in z-direction W = 1.

b) Derive the flow velocity, u, as a function of x.

c) If the ambient pressure is uniform (1 atm), compute the force to anchor the channel on the ground (again, for unit width of channel, W = 1). Be careful with the sign.

Problem 5. The height of a horizontal channel is y = 1/x, for 1 < x < 2, where x = 1 is the entrance and x = 2 the exit. Water flows into the channel with velocity uin = 2, as shown in the figure, where solid lines indicate the channel walls. The flow is in steady state. Assume that the flow is 1-D and u is uniform on each cross-section area.

a) If the fluid density is rho = 1000, compute the inlet mass flow rate per unit depth of the channel. i.e. the depth of the channel in z-direction W = 1.

b) Derive the flow velocity, u, as a function of x.

c) If the ambient pressure is uniform (1 atm), compute the force to anchor the channel on the ground (again, for unit width of channel, W = 1). Be careful with the sign.

Added by Shannon M.

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