In a horizontal water pipe that narrows to a smaller radius, the velocity of the water in the section with the smaller radius will be larger. What happens to the pressure? a) The pressure will be the same in both the wider and narrower sections of the pipe. b) The pressure will be higher in the narrower section of the pipe. c) The pressure will be higher in the wider section of the pipe d) It is impossible to tell.

The principle of conservation of mass states that the total mass entering a section of the pipe must be equal to the total mass exiting that section. Mathematically, this can be expressed as: A1V1 = A2V2 Where A1 and A2 are the areas of the wider and narrower sections, and V1 and V2 are the velocities in the wider and narrower sections, respectively.

Bernoulli's equation states that for an incompressible, steady flow and non-viscous fluid, the total energy (kinetic, potential, and pressure energy) along a streamline remains constant. Mathematically, this can be expressed as: P1 + 0.5 * ρ * V1^2 = P2 + 0.5 * ρ * V2^2 Where P1 and P2 are the pressures in the wider and narrower sections, ρ is the fluid density, and V1 and V2 are the velocities in the wider and narrower sections. In this exercise, the pipe is horizontal, so the potential energy due to height remains constant. Therefore, we can focus on the kinetic and pressure energy.

From the principle of conservation of mass (A1V1 = A2V2), we know that when the pipe narrows, the velocity of the water (V2) will be larger than the velocity in the wider section (V1). We can use this information and plug it into Bernoulli's equation: P1 + 0.5 * ρ * V1^2 = P2 + 0.5 * ρ * V2^2 To solve for the pressure difference between the two sections, we can rearrange the equation to obtain: P1 - P2 = 0.5 * ρ * (V2^2 - V1^2) As V2 > V1, the expression (V2^2 - V1^2) will be positive. This means that the pressure difference (P1 - P2) will also be positive. Therefore, the pressure will be higher in the wider section of the pipe (P1) compared to the narrower section (P2). So, the correct answer is: c) The pressure will be higher in the wider section of the pipe.